Graphs of Equations in Factored Form

Identify the form for the following Quadratic:

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

• Vertex Form

• Standard Form

• Factored Form

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 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.

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)

Compare f(x) to g(x). Which statement is true about the functions number of roots.

• f(x) has more roots than g(x)

• They both have 2 roots.

• They both have 0 roots.

• g(x) has more roots than f(x)

Compare f(x) to g(x). Which statement is true about their y-intercepts?

• f(x) has a negative y-intercept.

• g(x) has a negative y-intercept.

• They both have positive y-intercepts.

• They both have negative y-intercepts.

Compare g(x) to f(x). Which statement is true?

• g(x) has 2 negative x-intercepts.

• f(x) has one positive and one negative x-intercepts.

• f(x) has 2 positive x-intercepts.

• g(x) has 2 positive x-intercepts.

Compare g(x) to f(x). Which statement is true about their y-intercepts?

• Both y-intercepts are positive.

• g(x) has a positive y-intercept and f(x) has a negative.

• Both y-intercepts are negative.

• f(x) has a positive y-intercept and g(x) has a negative.

Compare g(x) to f(x). Which statement is true about their x-intercepts?

• g(x) and f(x) each have 2 x-intercepts.

• g(x) and f(x) each have 0 x-intercepts.

• g(x) has 2 x-intercepts and f(x) has 0.

• f(x) has 2 x-intercepts and g(x) has 0.