the axis of symmetry for the function $f(x) = -2x^2 + 4x + 1$ is the line $x = 1$. where is the vertex of…

the axis of symmetry for the function $f(x) = -2x^2 + 4x + 1$ is the line $x = 1$. where is the vertex of the function located?\n\n(0, 1)\n(1, 3)\n(1, 7)\n(2, 1)

the axis of symmetry for the function $f(x) = -2x^2 + 4x + 1$ is the line $x = 1$. where is the vertex of the function located?\n\n(0, 1)\n(1, 3)\n(1, 7)\n(2, 1)

Answer

Explanation:

Step1: Identify the x-coordinate of the vertex

The vertex of a parabola lies on its axis of symmetry. Given the axis of symmetry is $x = 1$, the x-coordinate of the vertex is $h = 1$. $$h = 1$$

Step2: Calculate the y-coordinate of the vertex

Substitute $x = 1$ into the function $f(x) = -2x^2 + 4x + 1$ to find the y-coordinate $k$. $$k = f(1) = -2(1)^2 + 4(1) + 1$$

Step3: Simplify the expression

Perform the arithmetic operations to find the value of $k$. $$k = -2(1) + 4 + 1 = -2 + 4 + 1 = 3$$

Step4: State the vertex coordinates

The vertex is represented by the point $(h, k)$. $$(h, k) = (1, 3)$$

Answer:

(1, 3)