Answer:
f(x) = 2(x - 5)² + 55 and f(x) = 2(x - 5)² - 45
Explanation:
The vertex form of a quadratic function is given by:
f(x) = a(x - h)^2 + k
In this equation:
"a" is the coefficient of the quadratic term.
(h, k) represents the coordinates of the vertex of the parabola.
Let's compare the given equations with the vertex form to determine which one matches:
f(x) = 2x² - 20x + 5
This is not in vertex form.
f(x) = 2(x - 5)² + 55
This is in vertex form with a = 2, h = 5, and k = 55.
f(x) = 2(x - 5)² - 45
This is in vertex form with a = 2, h = 5, and k = -45.
ƒ(x) = 2(x − 10)² + 5
This is not in vertex form.
f(x) = 2(x + 5)² – 45
This is in vertex form with a = 2, h = -5, and k = -45.
So, the equations that are in vertex form are:
f(x) = 2(x - 5)² + 55
f(x) = 2(x - 5)² - 45
f(x) = 2(x + 5)² – 45
The vertex form of the quadratic function is f(x) = 2(x - 5)² + 55 and f(x) = 2(x - 5)² - 45, which have the same vertex but different values for "k."