Question

fill in the missing spaces in the table below

features	$f(x) = -2x^2 + 8x + 1$	$g(x) = 3x^2 + 6x - 4$
vertex	$(2, \underline{\quad})$	$(\underline{\quad}, -7)$
axis of symmetry	$x = 2$	$\underline{\quad}$
maximum or minimum value	$\underline{\quad}$	minimum
opens upward or downward	$\underline{\quad}$	upward

features	$f(x) = -2x^2 + 8x + 1$	$g(x) = 3x^2 + 6x - 4$

Explanation:

Step1: Find f(x) y-intercept

Set $x=0$: $f(0) = -2(0)^2 + 8(0) + 1 = 1$

Step2: Find f(x) vertex y-value

Substitute $x=2$ into $f(x)$: $f(2) = -2(2)^2 + 8(2) + 1 = -8 + 16 + 1 = 9$

Step3: Find g(x) vertex x-value

Use vertex formula $x=-\frac{b}{2a}$: $x=-\frac{6}{2(3)} = -1$

Step4: Find g(x) axis of symmetry

Axis of symmetry = vertex x-value: $x=-1$

Step5: Determine f(x) max/min

$x^2$ coefficient is negative: maximum

Step6: Determine f(x) opening direction

$x^2$ coefficient is negative: downward

Answer:

Features	$f(x) = -2x^2 + 8x + 1$	$g(x) = 3x^2 + 6x - 4$
vertex	$(2, 9)$	$(-1, -7)$
axis of symmetry	$x=2$	$x=-1$
maximum or minimum value	maximum	minimum
opens upward or downward	downward	upward