Question

compare the parts below.
(a) graph the equation, $y=3x^2 + 23$. 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 $y=3x^2 + 23$ 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 $0\leq x\leq5$.
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: $\square \leq y \leq \square$
description:
the domain of $y=3x^2 + 23$ when the values of $x$ are restricted to $0\leq x\leq5$
the range of $y=3x^2 + 23$ when the values of $x$ are restricted to $0\leq x\leq5$
(c) find the p-intercept of the vertex $y=3x^2 + 23$. then choose the best description of the p-intercept.
p-intercept: $\square$
description:
the time when the price of the stock will reach $0$
the constant amount added to the stock price
the price of the stock when it is first available

Explanation:

Step1: Find vertex of parabola

For $y=3x^2+25$, vertex at $x=0$:
$y=3(0)^2+25=25$, so vertex is $(0,25)$

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

At $x=-1$: $y=3(-1)^2+25=28$, point $(-1,28)$
At $x=-2$: $y=3(-2)^2+25=37$, point $(-2,37)$

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

At $x=1$: $y=3(1)^2+25=28$, point $(1,28)$
At $x=2$: $y=3(2)^2+25=37$, point $(2,37)$

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

Min $y$ at $x=0$: $y=25$
Max $y$ at $x=5$: $y=3(5)^2+25=100$
Inequality: $25 \leq y \leq 100$

Step5: Identify vertex description

Vertex $(0,25)$ is the minimum point, so it represents the starting stock price.

Answer:

1. Plot points: $(0,25)$, $(-2,37)$, $(-1,28)$, $(1,28)$, $(2,37)$ then graph the parabola.
2. Inequality: $\boldsymbol{25 \leq y \leq 100}$

Description: The range of $y=3x^2+25$ when values of $x$ are restricted to $0\leq x\leq5$

1. y-intercept: $\boldsymbol{25}$

Description: The starting price of the stock when it becomes available