Roots from Quadratic Graph

Another name for the x-intercept

• Roots

• Zeros

• Solutions

• All of the above

Tags

CCSS.HSF-IF.C.7C

another name for x-intercept

• Zeros

• Vertex Form

• Quadratic Function

• Standard Form

Tags

CCSS.HSF-IF.C.7C

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)

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

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 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

Tags

CCSS.HSA-REI.B.4B

What are the solutions?

• -2, 1

• 1, 2

• -1,2

• 0,-4

What are the green dots called?

• axis of symmetry

• vertex

• parabola

• roots or x-intercepts

Tags

CCSS.HSF-IF.C.7A

If the graph of a quadratic does not intercept the x axis at any point, then it has:

• Real Solution

• Real Solutions

• Half a Solution

• No Real Solution

Tags

CCSS.HSF-IF.C.7A