Question

fill in the blanks enter intercepts as ordered pairs, aka points. then graph the parabola given in vertex form.
vertex form: $y = -(x + 4)^2 + 1$

1. does the parabola open up or down? $\bigcirc$ up $\bigcirc$ down
2. vertex $(x,y)$ =
3. equation of the axis of symmetry: $x = -4$

Explanation:

Step1: Find x-intercepts (y=0)

Set $y=0$, solve $0=-(x+4)^2+1$
$(x+4)^2=1$
$x+4=\pm1$
$x=-4+1=-3$ or $x=-4-1=-5$
So x-intercepts are $(-5,0)$ and $(-3,0)$

Step2: Find y-intercept (x=0)

Set $x=0$, calculate $y=-(0+4)^2+1$
$y=-16+1=-15$
So y-intercept is $(0,-15)$

Step3: Plot key points & graph

Plot vertex $(-4,1)$, intercepts $(-5,0), (-3,0), (0,-15)$, then draw a downward-opening parabola through these points, symmetric about $x=-4$.

Answer:

1. Down
2. $(-4, 1)$
3. $x=-4$

x-intercepts: $(-5, 0)$, $(-3, 0)$
y-intercept: $(0, -15)$
(Graph: A downward-opening parabola with vertex at $(-4,1)$, crossing the x-axis at $(-5,0)$ and $(-3,0)$, crossing the y-axis at $(0,-15)$, symmetric about the line $x=-4$)