Graphs in Factored Form

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)

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)

Match the equation to the graph. Remember to look at your roots, multiplicity, and end behavior!! Use your notes!

• y=-(x+1)(x-2)(x-4)

• y=(x+1)²(x-3)(x-1)³

• y = 3x³ – 2x + 1

• y=(x+1)³(x-3)(x-1)²

Remember to look at your roots, multiplicity, and end behavior!! Use your notes!

• y = ^_(x + 2)(x - 1)²

• y = -(x - 2)(x + 1)²

• y = (x - 2)(x + 1)²

• y = -x³

In the above graph, which root has a multiplicity of 2?

Remember to look at your roots, multiplicity, and end behavior!!

Use your notes!

• -1

• -3

• -120

• 4

What is the factored form of a function if it has zeros of 2, 3 and -1?

• (x-2)(x-3)(x+1)

• (x-1)(x-2)(x-3)

• (x-1)(x+2)(x+3)

• (x+1)(x+2)(x+3)

Identify the form for the following Quadratic:

y = -3(x - 2)(x - 6)

• Vertex Form

• Standard Form

• Factored Form

What is the equation in factored form of this graph?

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)