Question

1. $y=2x^2 - 16x + 30$

axis of symmetry: ____
vertex: ____
blank x-y table
blank coordinate grid

Explanation:

Step1: Find axis of symmetry

For quadratic $y=ax^2+bx+c$, axis is $x=-\frac{b}{2a}$.
Here $a=2$, $b=-16$, so:
$x=-\frac{-16}{2\times2}=\frac{16}{4}=4$

Step2: Find vertex y-coordinate

Substitute $x=4$ into $y=2x^2-16x+30$:
$y=2(4)^2-16(4)+30=2(16)-64+30=32-64+30=-2$

Step3: Make x-y value table

Choose x-values around $x=4$:

• $x=2$: $y=2(2)^2-16(2)+30=8-32+30=6$
• $x=3$: $y=2(3)^2-16(3)+30=18-48+30=0$
• $x=4$: $y=-2$
• $x=5$: $y=2(5)^2-16(5)+30=50-80+30=0$
• $x=6$: $y=2(6)^2-16(6)+30=72-96+30=6$

Answer:

Axis of Symmetry: $x=4$
Vertex: $(4, -2)$
x-y Table:

$x$	$y$
3	0
4	-2
5	0
6	6

(To graph: plot these points and draw a smooth parabola symmetric about $x=4$)