Question

What is the equation of the quadratic function with a vertex at (2,–25) and an x-intercept at (7,0)?

f(x) = (x – 2)(x – 7)
f(x) = (x + 2)(x + 7)
f(x) = (x – 3)(x + 7)
f(x) = (x + 3)(x – 7)

Answer 1

f(x) = (x + 3)(x – 7)

Explanation:

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Answer 2

"f(x) = (x + 3)(x – 7)"

Explanation:

If the vertex is (h,k), then the quadratic is can be written in the form:

y = a (x-h)^2 + k

So it will be:

y = a(x-2)^2 - 25

Now, to find a, we need the x-intercept (which is 7), so we plug in 7 into x and 0 into y and solve for a:

0 = a(7-2)^2 - 25

0 = a(5)^2 - 25

0 = 25a - 25

a = 1

THus, we can write:

y = (x-2)^2 - 25

Expanding this, we get:

y = x^2 -4x + 4 - 25

y = x^2 - 4x - 21

y = (x-7)(x+3)

THis is correct answer.