Question

select the correct answer.
which graph represents the solutions to this equation?
x² + 8x = -20
a.
graph of a parabola
b.
graph of a parabola

Explanation:

Step1: Rewrite equation in standard form

Rearrange to $y = x^2 + 8x + 20$

Step2: Find vertex (x-coordinate)

Use $x = -\frac{b}{2a}$, where $a=1$, $b=8$:
$x = -\frac{8}{2(1)} = -4$

Step3: Find vertex (y-coordinate)

Substitute $x=-4$ into $y = x^2 + 8x + 20$:
$y = (-4)^2 + 8(-4) + 20 = 16 - 32 + 20 = 4$

Step4: Check discriminant (real roots?)

Discriminant: $b^2 - 4ac = 8^2 - 4(1)(20) = 64 - 80 = -16$
Negative discriminant = no real x-intercepts, parabola opens upward (a>1) with vertex at $(-4, 4)$

Step5: Match to graphs

Graph A has x-intercepts and lower vertex; Graph B has vertex at (-4, ~4) with no x-intercepts.

Answer:

B. <The parabola with vertex at (-4, 4) opening upward, no x-intercepts>