Question

select the inequality which represents the graph shown below.
answer
\\( y - 10 \leq x^2 + 7x \\) \\( y - 10 \geq x^2 + 7x \\)
\\( y - 10 \leq x^2 - 7x \\) \\( y - 10 \geq x^2 - 7x \\)

Explanation:

Step1: Find parabola vertex

Vertex at $(3.5, -2.25)$

Step2: Write vertex form

$y = a(x-h)^2 + k$, so $y = a(x-3.5)^2 -2.25$

Step3: Solve for $a$ using y-intercept $(0,10)$

$10 = a(0-3.5)^2 -2.25$
$12.25 = 12.25a$
$a=1$

Step4: Expand to standard form

$y=(x-3.5)^2 -2.25$
$y=x^2 -7x +12.25 -2.25$
$y=x^2 -7x +10$
Rearrange to match options: $y-10=x^2-7x$

Step5: Determine inequality sign

Shaded area is above the parabola, so $y \geq x^2-7x+10$, or $y-10 \geq x^2-7x$

Answer:

$y - 10 \geq x^2 - 7x$