Question

Find the equation of the quadratic function with zeros 16 and 18 and vertex at (17, -2).

Answer 1

@phi

Answer 2

If you're asked to find a quadratic function, and they give you the zeroes a and b, then you can set up quadratic function like so:

(x - a)(x - b) = 0

In this case, you're given zeroes 16 and 18, so set up the equation like so:
(x - 16)(x - 18) = 0

This is true because if you use zero product property to solve for x you get:

x - 16 = 0
x - 18 = 0

and of course x = {16, 18}

Multiply the left side of the quadratic equation to get the form ax^2 + bx + c = 0

Then use the vertex formula \(\large x = -\frac{b}{2a}\) to find the x coordinate of the vertex.

If you get that far, I'll show you how to find the y coordinate of the vertex if you don't already know.

Answer 3

i lost you when you got to "multiply the left side of the quadratic equation.... etc" @Hero

Answer 4

The quadratic equation I was referring to was \((x - 16)(x - 18) = 0\).
Can you multiply \((x - 16)(x - 18)\) ?

Answer 5

x^2 - 18x - 16x + 288

Answer 6

Combine the like terms in the middle as well

Answer 7

x^2 - 34x + 288

Answer 8

so the answer is y = x^2 - 34x + 288

Answer 9

Well, you're supposed to check the vertex to make sure it is (-17, 2). But yes, it is correct.

Answer 10

thank you for your help! if you're free, i have another question i'm about to post, i'll give you another medal