Question

What is the function in Vertex of
f (x) = 15x^2 + 60x - 19



(
−
2
,
−
79
)
(−2,−79)

(
−
79
,
−
2
)
(−79,−2)

(
2
,
−
79
)
(2,−79)

(
79
,
2
)
(79,2)

Answer 1

To find the vertex of the quadratic function \( f(x) = 15x^2 + 60x - 19 \), we can use the vertex formula for a parabola given by \( f(x) = ax^2 + bx + c \).

The x-coordinate of the vertex can be found using the formula:

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

In this case, \( a = 15 \) and \( b = 60 \).

Calculating the x-coordinate of the vertex:

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

Next, we substitute \( x = -2 \) back into the function to find the y-coordinate of the vertex:

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

Therefore, the vertex of the function \( f(x) = 15x^2 + 60x - 19 \) is:

\[
(-2, -79)
\]

Among the options provided, the correct answer is:

\[
(-2, -79)
\]