Factored Form Quadratic 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 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.

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.

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)

Graph the following

y= (x-2)(x-4)

Tags

CCSS.HSA.CED.A.2

• F

• G

• H

• J

Tags

CCSS.HSF-IF.C.7A

What is a quadratic function in factored/intercept form with x-intercepts of (5,0) and (-2,0) that is normal size and opens up?

Mathematical Equivalence

ON

Tags

CCSS.HSF-IF.C.7A

What is a quadratic function in factored/intercept form with x-intercepts of (5,0) and (-2,0) that is normal size and opens up? f(x) = ________________

Mathematical Equivalence

ON

Identify the form for the following Quadratic:

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

• Vertex Form

• Standard Form

• Factored Form

Does this graph have a maximum or minimum value?

• maximum

• minimum

• neither

• both

Tags

CCSS.HSF-IF.C.7A