Chapter 4 Section 1Graphing Quadratic Equations in Standard

Form

In this assignment, you will be able to...

1. Graph a quadratic equation in the form y=ax^2,y=ax^2+c and y=ax^2+bx+c.

2. Determine if the graph opens up or opens down.

4. Determine if the function has a minimum or maximum value and calculate that value.

3. Find the vertex and axis of symmetry.

For the following function, tell whether the function opens up or opens down and state why.

y=3x^2-11.)

Answer: Opens up.

Because the coefficient for the x^2 is 3 and 3 is positive.Positive coefficients for x^2 opens up.

For the following function, tell whether the function opens up or opens down and state why.

2.) y=-x^2+5x+3

Answer: Opens down.

Because the coefficient for the x^2 is -1 and -1 is negative.Negative coefficients for x^2 opens down.

For the following function, tell whether the function opens up or opens down and state why.

3.) y=5x^2-27x

Answer: Opens up.

Because the coefficient for the x^2 is 5and 5 is positive.Positive coefficients for x^2 opens up.

For the following function, tell whether the function opens up or opens down and state why.

4.) y=-(1/2)x^2-(2/3)x+3

Answer: Opens down.

Because the coefficient for the x^2 is -1/2 and -1/2 is negative.

Negative coefficients for x^2 opens down.

For the following function, calculate the axis of symmetry

and find the vertex.

5.) y=-3x^2

Answer:y=-3x^2 is in the form y=ax^2. Since a=-3 and b=0,to find the axis of symmetry, you plug in -3 and 0 into

x=-b/(2a) and get x=-0/(2*-3) which equals 0.So the axis of symmetry is x=0.

To find the vertex, first know that the axis of symmetry isthe x value for your vertex. So x=0.

Plug in 0 for x in y=-3x^2.Calculate y, y=-3(0)^2. So y=0.

Therefore, the vertex is (0,0).

For the following function, calculate the axis of symmetry

and find the vertex.

6.) y=4x^2+3

Answer:y=4x^2+3 is in the form y=ax^2+c. Since a=4 and b=0,

to find the axis of symmetry, you plug in 4 and 0 intox=-b/(2a) and get x=-0/(2*4) which equals 0.

So the axis of symmetry is x=0.To find the vertex, first know that the axis of symmetry is

the x value for your vertex. So x=0. Plug in 0 for x in y=4x^2+3.

Calculate y, y=4(0)^2+3. So y=3. Therefore, the vertex is (0,3).

For the following function, calculate the axis of symmetry

and find the vertex.

7.) y=-2x^2-4x+2

Answer:y=-2x^2-4x+2 is in the form y=ax^2+bx+c.

Since a=-2, b=-4 and c=2, to find the axis of symmetry,you plug in -2 for a and -4 for b into x=-b/(2a).

So you get x=-(-4)/(2*-2)which equals -1. So the axis of symmetry is x=-1.

To find the vertex, first know that the axis of symmetry isthe x value for your vertex. So x=-1.

Plug in -1 for x in y=-2x^2-4x+2.Calculate y, y=-2(-1)^2-4(-1)+2. So y=4.

Therefore, the vertex is (-1,4).

Graph the equation. Label the vertex and axis of symmetry.

8.) y=x^2-3

Answer: Graph y=x^2-3. First calculate the axis of symmetry. Plug in a=1 and b=0 into

x=-b/(2a). So x=-0/(2*1) or x=0. So your axis of symmetry is

x=0.Now plug in x=0 into y=x^2-3. So y=0^2-3 and

y=-3.Now your vertex is (0,-3).

Next, make a T-Chart with 2 points above and

belowthe vertex. Find your y.

values. Plot the points on the graph.

Label your axis of symmetry and vertex.

Graph the equation. Label the vertex and axis of symmetry.

9.) y=-2x^2+4x

Answer: Graph y=-2x^2+4x. First calculate the axis of symmetry. Plug in a=-2 and b=4 into x=-

b/(2a). So x=-4/(2*-2) or x=1. So your axis of symmetry is

x=1.Now plug in x= into y=-2x^2+4x. So y=-

2*(1)^2+4(1) which means y=2. So your vertex is (1,2).

Next, make a T-Chart with 2 points above and

belowthe vertex. Find your y

values. Plot the points on the graph.

Label your axis of symmetry and vertex.

Graph the equation. Label the vertex and axis of symmetry.

10.)y=-3x^2-12x+1

Answer: Graph y=-3x^2-12x+1. First calculate the axis of symmetry. Plug in a=-3 and b=-12

into x=-b/(2a). So x=-(-12)/(2*-3) or x=-2. So your axis of symmetry

is x=-2.Now plug in x=-2 into y=-3x^2-12+1. So y=-3*(-

2)^2-12(-2)+1 which is y=13. So your vertex is (-2,13).

Next, make a T-Chart with 2 points above and

belowthe vertex. Find your y.

values. Plot the points on the graph.

Label your axis of symmetry and vertex.

Graph the equation. Label the vertex and axis of symmetry.

11.) y=2x^2-8x+1

Answer:y=2x^2-8x+1

Graph the equation. Label the vertex and axis of symmetry.

12.) y=4x^2-16x+3

Answer: y=4x^2-16x+3

Minimize Cost. A baker modeled the monthly operating costs for making wedding cakes by

the function y=0.5x^2-12x+150 where y is the total

cost in dollars and x is the number of cakes prepared.

a.). Find the vertex and axis of symmetry.

b.). What is the minimum cost?

c.). How many wedding cakes should be made to yield the minimum cost?

13.)

Answer:

a.) Vertex (12,78) AOS x=12

b.) $78

c.). 12 cakes

14.)A ball travels along the function y=-4x^2+24x feet.

b.)What is the maximum height the ball will reach?

a.) Graph the equation. Label the vertex and axis of

symmetry.

c.) How far did the ball travel?

a.). Vertex (3,36) AOS x=3

Answer:

b.) The maximum height is 36 feet.

c.) The ball will travel 6 feet.

15.)On a separate sheet of paper, describe how to graph the equation y=-2x^2-6x-3

a.) Describe how to determine if the graph opens up or down.

b.) Describe how to find the and axis of symmetry.

c.)Describe if you have a minimum or maximum valueand calculate the value.

You have finished 4-1