Question

What is the equation of the quadratic function that has a minimum at (7, -3) and passes through (9, 9)?

a) y = -2x² + 2x + 7
b) y = 2x² - 2x + 7
c) y = -2x² + 2x - 7
d) y = 2x² - 2x - 7

Answer 1

The quadratic equation with a minimum at (7, -3) and passing through (9, 9) is y = 3(x - 7)^2 - 3, in vertex form.

Step-by-step explanation:

The question is asking for the equation of a quadratic function that has a minimum at the point (7, -3) and also passes through another point, (9, 9). To find this equation, we will use the vertex form of a quadratic equation, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Here, we have the vertex (7, -3), so our equation will start with y = a(x - 7)^2 - 3. To find the value of 'a', we will plug in the coordinates of the other point (9, 9).

9 = a(9 - 7)^2 - 3

9 = 4a - 3

a = 3

So, a = 3.

Substituting 'a' back into the vertex form, we get the equation: y = 3(x - 7)^2 - 3.