![Page 1: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/1.jpg)
Graphing Graphing Quadratic Quadratic FunctionsFunctions
![Page 2: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/2.jpg)
2 Forms of Quadratic Equations
y = ax2 + bx + c
y = a(x – h)2 + kStandard
FormVertex Form
![Page 3: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/3.jpg)
The axis of symmetry for the parabola is the vertical line through the vertex.
![Page 4: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/4.jpg)
Graphing Using Vertex Form
y = a(x – h)2 + k
Vertex: (h, k)
Axis of symmetry: x = h
VERTICAL LINEIf a is positive, then it opens up.
If a is negative, then it opens down.
![Page 5: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/5.jpg)
Graphing Using Vertex Form
1.Find and sketch the axis of symmetry (opposite of h).
2.Find and plot your vertex (opposite of h, same as k).
3.Construct a table of values to find 2 points on one side of the axis of symmetry (choose 2 x-values above your symmetry value)
![Page 6: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/6.jpg)
Graphing Using Vertex Form
4. Use Symmetry to plot the points on the opposite side of your axis of symmetry.
5. Connect them with a U-shaped curve
![Page 7: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/7.jpg)
Tell whether it opens up or down, axis of symmetry, and name the vertex.
f(x)= -3(x – 2)2 + 5
Vertex: (2, 5)
Axis of symmetry: x = 2
Opens DOWN
a = -3
h = 2 k = 5
y = a(x – h)2 + k.
![Page 8: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/8.jpg)
f(x) = (x + 4)2 – 6a = 1 h = -4 k = -6
Tell whether it opens up or down, axis of symmetry, and name the vertex.
Vertex: (-4, -6)
Axis of symmetry: x = -4Opens UP
You try…
![Page 9: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/9.jpg)
x 2(x + 5)2 - 4
y (x, y)
2f 2( 5) 4x x
Graph
![Page 10: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/10.jpg)
x y (x, y)
21f ( 3) 1
2x x
Graph
21( 3) 1
2x
![Page 11: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/11.jpg)
Graphing Using Standard Form
*Once it is in standard form:1.Find and sketch the axis of symmetry using 2.Find your vertex by substituting your axis of symmetry back into the original equation and solve for y.
a
bx
2
![Page 12: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/12.jpg)
Graphing Using Standard Form
4. Construct a table of values to find 2 points on one side of the axis of symmetry (choose 2 x-values above your symmetry value)
5. Use Symmetry to plot the points on the opposite side of your axis of symmetry.
6. Connect them with a U-shaped curve
*Remember: If a is positive, it opens up, if a is negative, it opens down.
![Page 13: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/13.jpg)
x (x)2 + 8x + 13
y (x, y)
2f 8 13x x x
x b2a
Graph
![Page 14: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/14.jpg)
x -(x)2 + 2x y (x, y)
2f 2x x x
x b2a
Graph
![Page 15: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/15.jpg)
Converting From Converting From Vertex Form to Vertex Form to Standard Form:Standard Form:y = (x – 3)2 + 5
Step 1: FOIL the binomialStep 2: Multiply the “a” term
by what you just foiledStep 3: combine like terms!
![Page 16: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/16.jpg)
Convert the following to Convert the following to standard form:standard form:
y = 2(x – 4)2 + 6
![Page 17: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/17.jpg)
Convert the following to Convert the following to standard form:standard form:
y = (x + 3)² + 4
![Page 18: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/18.jpg)
Step 1: Identify a, b, and cStep 2: find the vertex (h, k)
x-coordinate (h) =
y-coordinate (k) = substitute the value you found for the x coordinate.
Step 3: Substitute a, h, and k into vertex form!
2
ba
Converting From Converting From Standard Form to Standard Form to
Vertex FormVertex Form
![Page 19: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/19.jpg)
Convert the following to vertex form:Convert the following to vertex form:
![Page 20: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/20.jpg)
What is the vertex form of a What is the vertex form of a parabola whose standard parabola whose standard form equation is:form equation is:
![Page 21: Graphing Quadratic Functions. 2 Forms of Quadratic Equations y = ax 2 + bx + c y = a(x – h) 2 + k Standard Form Vertex Form](https://reader035.vdocuments.net/reader035/viewer/2022081513/56649f1f5503460f94c38239/html5/thumbnails/21.jpg)
Convert the following to vertex form:Convert the following to vertex form: