Question

What is the function in Vertex form:

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


f
(
x
)
=
15
(
x
+
2
)
2
−
79
f(x)=15(x+2)
2
−79

f
(
x
)
=
79
(
x
+
2
)
2
−
15
f(x)=79(x+2)
2
−15

f
(
x
)
=
−
15
(
x
+
2
)
2
−
79
f(x)=−15(x+2)
2
−79

f
(
x
)
=
−
15
(
x
+
2
)
2
+
79
f(x)=−15(x+2)
2
+79

Answer 1

To convert the given function \( f(x) = 15x^2 + 60x - 19 \) into vertex form, we need to complete the square.

1. Start with the original function:
\[
f(x) = 15x^2 + 60x - 19
\]

2. Factor out the coefficient of \( x^2 \) (which is 15) from the first two terms:
\[
f(x) = 15(x^2 + 4x) - 19
\]

3. Now, we need to complete the square inside the parentheses. Take half of the coefficient of \( x \) (which is 4), square it, and add and subtract it inside the parentheses:
- Half of 4 is 2, and its square is \( 2^2 = 4 \).

Thus, we have:
\[
f(x) = 15(x^2 + 4x + 4 - 4) - 19
\]
\[
= 15((x + 2)^2 - 4) - 19
\]

4. Simplify:
\[
= 15(x + 2)^2 - 15 \cdot 4 - 19
\]
\[
= 15(x + 2)^2 - 60 - 19
\]
\[
= 15(x + 2)^2 - 79
\]

The vertex form of the function is:
\[
f(x) = 15(x + 2)^2 - 79
\]

So, the correct option from your provided choices is:
\[
f(x) = 15(x + 2)^2 - 79
\]