8 which point lies on the graph of $y = 3x^2 - \frac{1}{4}x + 3$? (1) $(-2, 15.5)$ (2) $(-1, 5.75)$ (3) $(1, 6.25)$ (4) $(2, 15.5)$ skill #4: statistics - mean, median, mode and range median is the middle number mode is the number that shows up the most range is the biggest number - the smallest number iqr is the 3rd quartile - the 1st quartile

Question

Accepted Answer

# Explanation:
To determine which point lies on the graph of $ y = 3x^2 - \frac{1}{4}x + 3 $, we substitute the $ x $-coordinate of each point into the equation and check if the resulting $ y $-value matches the given $ y $-coordinate.

## Step 1: Check Point (1) $(-2, 15.5)$
Substitute $ x = -2 $ into the equation:
$$
\begin{align*}
y &= 3(-2)^2 - \frac{1}{4}(-2) + 3 \
&= 3(4) + \frac{2}{4} + 3 \
&= 12 + 0.5 + 3 \
&= 15.5
\end{align*}
$$
The calculated $ y $-value is $ 15.5 $, which matches the given $ y $-coordinate of the point $(-2, 15.5)$. Let's verify the other points for completeness.

## Step 2: Check Point (2) $(-1, 5.75)$
Substitute $ x = -1 $ into the equation:
$$
\begin{align*}
y &= 3(-1)^2 - \frac{1}{4}(-1) + 3 \
&= 3(1) + \frac{1}{4} + 3 \
&= 3 + 0.25 + 3 \
&= 6.25
\end{align*}
$$
The calculated $ y $-value is $ 6.25 $, which does not match $ 5.75 $.

## Step 3: Check Point (3) $(1, 6.25)$
Substitute $ x = 1 $ into the equation:
$$
\begin{align*}
y &= 3(1)^2 - \frac{1}{4}(1) + 3 \
&= 3 - 0.25 + 3 \
&= 5.75
\end{align*}
$$
The calculated $ y $-value is $ 5.75 $, which does not match $ 6.25 $.

## Step 4: Check Point (4) $(2, 15.5)$
Substitute $ x = 2 $ into the equation:
$$
\begin{align*}
y &= 3(2)^2 - \frac{1}{4}(2) + 3 \
&= 3(4) - 0.5 + 3 \
&= 12 - 0.5 + 3 \
&= 14.5
\end{align*}
$$
The calculated $ y $-value is $ 14.5 $, which does not match $ 15.5 $.

# Answer:
(1) $(-2, 15.5)$

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QUESTION IMAGE

Question

Explanation:

Step 1: Check Point (1) \((-2, 15.5)\)

Step 2: Check Point (2) \((-1, 5.75)\)

Step 3: Check Point (3) \((1, 6.25)\)

Step 4: Check Point (4) \((2, 15.5)\)

Answer: