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

Answer 1

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

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

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

3. Complete the square inside the parentheses. To do this, take half of the coefficient of \( x \), which is \( 4 \), divide it by 2 to get \( 2 \), and square it to get \( 4 \). Add and subtract \( 4 \) inside the parentheses:
\[
f(x) = 15(x^2 + 4x + 4 - 4) - 19
\]

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

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

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

**Answer**: \( f(x) = 15(x + 2)^2 - 79 \)