Quadratic Equations from Graphs

Write a quadratic equation given the x intercepts and one other point.

Step 1: Write the factors.

The intercepts of this function are (6, 0) and (8, 0). Write the factors.

• (x-6) and (x-8)

• (x+6) and (x+8)

• (x-6) and (x+8)

• (x+6) and (x-8)

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Write a quadratic equation given the x intercepts and one other point. Step 3: Write the equation in factored form. Now, you know that the factors are (x-6) and (x-8) and a = -1. Write the equation of the graph in factored form.

• -(x-6)(x-8)

• -(x+6)(x+8)

• (x-6)(x+8)

• (x+6)(x-8)

Write a quadratic equation given the x intercepts and one other point.

Step 2: Find a.

Now that you know that the factors are (x-6) and (x-8), you must find a. Plug the coordinates of the vertex (7, 1) in for x and y and solve for a.

y = a(x-6)(x-8)

What is the value of a?

• a = 1

• a = -1

• a = 7

• a = -7

Write a quadratic equation given the x intercepts and one other point.

Put the steps together.

1. Find the factors.
2. Solve for a by substituting in the extra point.
3. Write the equation in factored form.

The roots of the function are (-3, 0) and (5, 0).

The point (4, -3) is also on the graph.

• y=4(x+3)(x-5)

• y=3/7(x-3)(x+5)

• y=-3(x-3)(x+5)

• y=3/7(x+3)(x-5)

Use the graph to solve the equation: x²+x-6=0

• x= -6

• x=0

• x=3 and x= -2

• x= -3 and x=2

• -2

• 1

• 17

• 0

• 5

• -1

• -27

Tags

CCSS.HSA-REI.B.4B

• -1 and 3
• 1 and -3
• -1 and -3
• 1 and 3

Use the graph of the function f(x)=-2x²+4x+6 to find the solution(s) of the equation -2x²+4x+6=0.

• x=-1

• x=3

• x=-1 and x=3

• x=1and x=8 

Which quadratic equation gives the graph below?

Given a graph, how can you find the "solutions" to a quadratic?

• Copy off neighbor

• Plug into calculator

• Solutions are where the quadratic crosses the x axis

• Magic 8 Ball