Question

this question has two parts. the equation of a quadratic function is given, in standard form. \\( f(x) = 2x^2 - 8x + 5 \\) part a write the equation that represents the axis of symmetry for the given quadratic equation. axis of symmetry: \\( 2 \\) part b what are the coordinates of the vertex of the function? enter the coordinates. vertex: (\\( 2 \\), \\( -3 \\))

Explanation:

Step1: Recall axis of symmetry formula

For quadratic $f(x)=ax^2+bx+c$, axis is $x=-\frac{b}{2a}$

Step2: Identify $a, b$ from given function

Given $f(x)=2x^2-8x+5$, so $a=2$, $b=-8$

Step3: Calculate axis of symmetry

$x=-\frac{-8}{2\times2}=\frac{8}{4}=2$

Step4: Find vertex x-coordinate

Vertex lies on axis of symmetry, so $x=2$

Step5: Calculate vertex y-coordinate

Substitute $x=2$ into $f(x)$:
$f(2)=2(2)^2-8(2)+5=2(4)-16+5=8-16+5=-3$

Answer:

Part A: $x=2$
Part B: $(2, -3)$