Find Quadratic Equation Given Graph

Given the vertex, V(-4,-2), of a quadratic equation, find the equation if the graph passes through the point (-2,-6).

• ƒ(x) = -(x+4)²-2

• ƒ(x) = (x+4)²-2

• ƒ(x) = -(x-4)²-2

• ƒ(x) = (x-4)²+2

Which equation could match the graph?

• y = (x + 1)(x + 4)

• y = (x - 1)(x - 4)

• y = (x - 4)(x - 4)

• y = (x + 2.5)(x + 4)

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)

Which of the following equations matches standard form of a quadratic?

• ax + by = c

• y = a(x - h)² + k

• y = ax² + bx + c

• y = mx + b

What are the solutions of the quadratic equation represented by the graph?

• -2 and 3

• -1/2 and -6

• -2 and -6

• 3 and -6

What are the solution(s)?

• x=3

• x=7

• x=5

• x=-4

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)

Write a quadratic equation in vertex form given the vertex and another point.

1. Substitute the coordinates of the vertex (1, -4) in for h and k.

Vertex form: y=a(x-h)²+k

• (x+1)²-4=y

• (x-1)²-4=y

• (x + 1)(x - 3)=y

• x2 +2x - 3=y