Question

The graph of a quadratic function passes through (-2, 0), (2, 0), and (0, 8). What is the

function?
f(x) =____

Answer 1

The quadratic function passing through (-2, 0), (2, 0), and (0, 8) is f(x) = -x^2 + 8.

Step-by-step explanation:

The graph of a quadratic function passing through (-2, 0), (2, 0), and (0, 8) can be represented by the equation f(x) = ax^2 + bx + c. We can substitute the given points into the equation to find the values of a, b, and c.

Using the point (-2, 0), we get 0 = 4a - 2b + c. Using the point (2, 0), we get 0 = 4a + 2b + c. Using the point (0, 8), we get 8 = c.

Substituting the value of c into the first two equations, we can solve for a and b. By solving these equations, we find that a = -1 and b = 0. Therefore, the quadratic function is f(x) = -x^2 + 8.

Answer 2

y = -2x^2 + 8

Step-by-step explanation:

It is clear from the information that (-2, 0) and (2, 0) are the zeros of the quadratic equation, while (0,8) is the vertex.

Thus, we can find the equation of the quadratic function using the vertex form which is

`y = a(x-h)^2+k`, where y and x are any x and y coordinate on the parabola, and h and k are the coordinate of the vertex.

We can plug in (-2, 0) for x and y and (0, 8) for h and k. This means we simply need to solve for a:

`0=a(-2-0)^2+8\\0=a(-2)^2+8\\0=4a+8\\-8=4a\\-2=a\\`

Thus, our equation is y = -2x^2 + 8