Question

You are asked to graph a parabola given the equation  y=14x2−2x+7 . At which point would you graph the vertex of the parabola?(1 point)Responses(4,2)left parenthesis 4 comma 2 right parenthesis(4,1)left parenthesis 4 comma 1 right parenthesis(4,3)left parenthesis 4 comma 3 right parenthesis(4,4)

Answers

GPT-4o mini
To determine the vertex of the parabola given by the equation \( y = 14x^2 - 2x + 7 \), we can use the formula for the x-coordinate of the vertex of a parabola given by the standard form \( y = ax^2 + bx + c \). The formula is:

\[
x = -\frac{b}{2a}
\]

In this case:

- \( a = 14 \)
- \( b = -2 \)

Now we can find the x-coordinate of the vertex:

\[
x = -\frac{-2}{2 \cdot 14} = \frac{2}{28} = \frac{1}{14}
\]

Next, we substitute \( x = \frac{1}{14} \) back into the equation to find the y-coordinate of the vertex:

\[
y = 14\left(\frac{1}{14}\right)^2 - 2\left(\frac{1}{14}\right) + 7
\]
\[
= 14\left(\frac{1}{196}\right) - \frac{2}{14} + 7
\]
\[
= \frac{14}{196} - \frac{2}{14} + 7
\]
\[
= \frac{1}{14} - \frac{1}{7} + 7
\]
\[
= \frac{1}{14} - \frac{2}{14} + \frac{98}{14}
\]
\[
= \frac{1 - 2 + 98}{14}
\]
\[
= \frac{97}{14}
\]

Thus, the vertex of the parabola is at the point \(\left(\frac{1}{14}, \frac{97}{14}\right)\).

None of the provided response options \((4,2), (4,1), (4,3), (4,4)\) contain the correct vertex.

Therefore, the vertex \(\left(\frac{1}{14}, \frac{97}{14}\right)\) does not match any of the given options. Please double-check the response options.

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