IB Math Studies Yr 1

Name_________________________________ Date_______________ 5-3 Solving Systems of Equations with Quadratics

Today’s Learning Goals:

How can I solve a system of equations using the calculator?

Warm Up: On the grid below, graph the lines 𝑥 = −4 and 𝑦 = 2.

Linear – Quadratic System This familiar linear- quadratic system, where only one variable is squared in the quadratic, will be the

graph of a parabola and a straight line.

When a parabola and a straight line are graphed on the same set of axes, three situations are possible.

Number of Solutions: Solution set:

Number of Solutions: Solution set:

Number of Solutions: Solution set:

a) How many solutions are there in this system of equations? b) What is the solution to this system of equations? c) What are we looking for when we are asked to find the solution of a system of equations?

IB Math Studies Yr 1

1. The graph of the function𝑦 = 𝑓(𝑥) is graphed to the right. (a) On the same grid, graph 𝑦 = −3

(b) Write down the coordinates of the points of intersection. (c) On the same grid, graph 𝑦 = −2

*How would you find the intersections between 𝒇(𝒙) And 𝒚 = −𝟐?*

Finding Points of Intersection In the calculator! 1. Plug our equations into our calculator for Y1 and Y2 2. Hit zoom → 6 3. Go to 2nd Trace 4. Select option 5: Intersect 5. Go to the one of the points of intersection using your

left and right arrow keys 6. Hit Enter 3 times! 7. Repeat steps 3, 4, 5, 6 if there is more than one intersection!

Example: Solve the following system of equations: 𝑓(𝑥) = 5 + 3𝑥 − 𝑥2 and 𝑦 = 2𝑥 + 3

IB Math Studies Yr 1

1. The graph of the function 𝑓(𝑥) = −2𝑥2 − 4𝑥 + 6 is shown below.

(a) On the same grid, graph 𝑦 = 5 (b) Write down the coordinates of the points of intersection.

2. The graph of the function 𝑓(𝑥) =2

3𝑥2 − 4𝑥 + 7 is shown below.

Line 𝐿 intersects the y-axis at 6 and has a gradient of −2. (a) On the same grid, graph line 𝐿. (b) Write down the coordinates of the points of intersection.

IB Math Studies Yr 1

PUTTING IT ALL TOGETHER This is a question that combines content from Unit 4 and Unit 5

The graph of a line 𝐿 passing through (1,1) and (2, 3) and the graph of a parabola P

has the function 𝑃(𝑥) = 𝑥2 − 3𝑥 − 4.

a) Find the gradient of line L.

b) Write the equation of line L in the form 𝑦 = 𝑚𝑥 + 𝑐.

The graphs of line L and parabola P intersect at approximately (5.54, 10.1).

c) State the coordinates of the other point of intersection.