Given Graph Find the Quadratic Equation

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

What type of function is shown in the table above?

• Linear

• Quadratic

• Exponential

• None

What type of function is shown above?

• Linear

• Quadratic

• Exponential

• None

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 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 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. 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)

If the blue is f(x)=x^2, the red must be

• g(x)=(x+3)²

• g(x)=(x-3)²

• g(x)=x²+3

• g(x)=x²-2

If the blue is f(x)=x^2, then the red must be

• g(x)=x² - 5

• g(x)=x² + 5

• g(x)=(x - 5)²

• g(x)=(x + 5)²