Question

a stockbroker uses the quadratic function to model the price of a stock.
in the function the price p (in dollars) is a function of t, the number of minutes after the stock becomes available on the market.
$p=5t^2 + 25$
complete the parts below.
(a) graph the parabola $y=5x^2 + 25$. 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 $y=5x^2 + 25$ 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 this inequality.
inequality: $25 \leq y \leq 100$
description:
$odot$ the domain of $y=5x^2 + 25$ when the values of x are restricted to $0\leq x\leq 5$
$circ$ the range of $y=5x^2 + 25$ when the values of x are restricted to $0\leq x\leq 5$
(c) find the y-intercept of the graph $y=5x^2 + 25$. then choose the best description of the y-intercept.
y-intercept: 25
description:
$circ$ the least (lowest) price of the stock when $t=0$
$circ$ the highest price of the stock that occurs
$odot$ the price of the stock (in dollars) when it is first available

Explanation:

Step1: Identify parabola vertex

For $y=5x^2 + 25$, vertex at $x=0$:
$y=5(0)^2 +25=25$, so vertex $(0,25)$

Step2: Find left points (x=-1,-2)

At $x=-1$: $y=5(-1)^2+25=30$, point $(-1,30)$
At $x=-2$: $y=5(-2)^2+25=45$, point $(-2,45)$

Step3: Find right points (x=1,2)

At $x=1$: $y=5(1)^2+25=30$, point $(1,30)$
At $x=2$: $y=5(2)^2+25=45$, point $(2,45)$

Step4: Find range for 0≤x≤5

Min y at x=0: $y=25$
Max y at x=5: $y=5(5)^2+25=150$
Range: $25\leq y\leq150$

Step5: Identify y-intercept

Y-intercept at $x=0$: $y=25$

Answer:

(a) Plotted points:

Vertex: $(0, 25)$
Left points: $(-1, 30)$, $(-2, 45)$
Right points: $(1, 30)$, $(2, 45)$

(b)

Inequality: $25 \leq y \leq 150$
Description: The range of $y=5x^2 +25$ when the values of $x$ are restricted to $0\leq x\leq5$

(c)

y-intercept: $25$
Description: The price of the stock (in dollars) when it is first available