Factors and X-Intercepts

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 the equation of the quadratic function that has a x-intercepts at 2 and 4 and passes through the point (3, 4).

• y = -4(x - 2)(x - 4)

• y = -4(x + 2)(x + 4)

• y = 4(x - 2)(x - 4)

• y = -0.25(x - 2)(x - 4)

Write the equation of the quadratic function that has a x-intercepts at 9 and 1 and passes through the point (0, -18).

• y = x² + 9x - 18

• y = -2(x - 9)(x - 1)

• y = -2(x + 9)(x + 1)

• y = 2(x + 9)(x + 1)

This is what form? y = 5(x+2)(x-1)

• Standard

• Vertex

• Factored

• None of These

Write the equation of the quadratic function in intercept form (factored).

• y = (x + 1)(x - 1)

• y = x² + 1

• y = ( x - 1 )²

• y = ( x + 1 )²

Which equation represents this graph.

• f(x)=(x - 4)² - 3

• f(x)=-(x - 4)² + 3

• f(x)=(x - 4)² + 3

• f(x)=-(x + 4)² + 3

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

Now, take the factored form and write it in Standard Form (ax²+bx+c=0) by double distributing (or FOIL).

• x²+2x-15=0

• -x²+14x -48=0

• - x²+8x-15=0

• x² + 5x -16=0

Write a quadratic equation given the x intercepts and one other point. Put the steps together. Find the factors. Solve for a by substituting in the extra point. 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 any method (graph, factor, complete the square, quadratic formula) to solve the function:

f(x)=x²-7x+10

• No solutions

• x=-2 and x=-5

• x=2 and x=5

• x = 2/5