Question

complete the parts below.
(a) graph the parabola $y = 3x^2 + 25$. to do so, plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. then click on the graph-a-function button.
(b) the function $y = 3x^2 + 25$ accurately models the price of the stock only for the first 5 minutes the stock is available on the market. that is, the model is accurate only for $0 \leq x \leq 5$.
fill in the blanks below to write an inequality for all the values of $y$ given by the model over those 5 minutes. then choose the best description of the inequality.
inequality: $\square \leq y \leq \square$
description:
the domain of $y = 3x^2 + 25$ when the values of $x$ are restricted to $0 \leq x \leq 5$
the range of $y = 3x^2 + 25$ when the values of $x$ are restricted to $0 \leq x \leq 5$
(c) the content is incomplete, but it is a related question about $y = 3x^2 + 25$

Explanation:

Step1: Find parabola vertex

For $y = ax^2 + k$, vertex is $(0,k)$. Here $a=-5, k=25$, so vertex: $(0,25)$

Step2: Find left vertex points

Choose $x=-1, x=-2$:
$x=-1$: $y=-5(-1)^2+25=20$ → $(-1,20)$
$x=-2$: $y=-5(-2)^2+25=5$ → $(-2,5)$

Step3: Find right vertex points

Choose $x=1, x=2$:
$x=1$: $y=-5(1)^2+25=20$ → $(1,20)$
$x=2$: $y=-5(2)^2+25=5$ → $(2,5)$

Step4: Find range for $0\leq x\leq5$

Minimum $y$ at $x=5$: $y=-5(5)^2+25=-100$
Maximum $y$ at $x=0$: $y=25$
Range inequality: $-100\leq y\leq25$

Answer:

(a) Plot the points: $(0,25)$, $(-1,20)$, $(-2,5)$, $(1,20)$, $(2,5)$ then draw the downward-opening parabola through them.
(b) Inequality: $\boldsymbol{-100\leq y\leq25}$
Description: The range of $y=-5x^2 + 25$ when the values of $x$ are restricted to $0\leq x\leq5$