Question
The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located?
(0, 1)
(1, 3)
(1, 7)
(2, 1)
(0, 1)
(1, 3)
(1, 7)
(2, 1)
Answers
GPT-4o mini
To find the vertex of the quadratic function \( f(x) = -2x^2 + 4x + 1 \), we can use the fact that the axis of symmetry is given by the equation \( x = -\frac{b}{2a} \), where \( a \) and \( b \) are the coefficients from the standard form \( ax^2 + bx + c \).
In this case, \( a = -2 \) and \( b = 4 \).
We know that the axis of symmetry is \( x = 1 \). We can directly find the vertex by substituting \( x = 1 \) back into the function \( f(x) \):
\[
f(1) = -2(1)^2 + 4(1) + 1
\]
Calculating this step-by-step:
\[
f(1) = -2(1) + 4 + 1
\]
\[
f(1) = -2 + 4 + 1
\]
\[
f(1) = 3
\]
Thus, the vertex of the function is located at \( (1, 3) \).
Therefore, the answer is \( (1, 3) \).
In this case, \( a = -2 \) and \( b = 4 \).
We know that the axis of symmetry is \( x = 1 \). We can directly find the vertex by substituting \( x = 1 \) back into the function \( f(x) \):
\[
f(1) = -2(1)^2 + 4(1) + 1
\]
Calculating this step-by-step:
\[
f(1) = -2(1) + 4 + 1
\]
\[
f(1) = -2 + 4 + 1
\]
\[
f(1) = 3
\]
Thus, the vertex of the function is located at \( (1, 3) \).
Therefore, the answer is \( (1, 3) \).