Question

What is the function in Vertex of

f(x) =15x^2 =60x-19


(
−
2
,
−
79
)
(−2,−79)

(
2
,
−
79
)
(2,−79)

(
79
,
2
)
(79,2)

(
−
79
,
−
2
)
(−79,−2)

Answer 1

To find the vertex of the quadratic function given by the equation

\[
f(x) = 15x^2 - 60x - 19,
\]

we can use the vertex formula for a parabola in the form \( ax^2 + bx + c \). The x-coordinate of the vertex can be found using the formula:

\[
x = -\frac{b}{2a},
\]

where \( a \) is the coefficient of \( x^2 \) and \( b \) is the coefficient of \( x \).

In this case:

- \( a = 15 \)
- \( b = -60 \)

Substituting the values into the formula:

\[
x = -\frac{-60}{2 \cdot 15} = \frac{60}{30} = 2.
\]

Next, we need to find the corresponding y-coordinate by substituting \( x = 2 \) back into the function \( f(x) \):

\[
f(2) = 15(2^2) - 60(2) - 19.
\]
\[
f(2) = 15(4) - 120 - 19.
\]
\[
f(2) = 60 - 120 - 19.
\]
\[
f(2) = -60 - 19 = -79.
\]

So the vertex of the function is:

\[
(2, -79).
\]

Therefore, the correct answer is:

**(2, -79)**