Question

Graph the quadratic y=4x2+3x−8
. What is the vertex of this quadratic?(1 point)
Responses

(−1.838,0)
left parenthesis negative 1.838 comma 0 right parenthesis

(1.088,0)
left parenthesis 1.088 comma 0 right parenthesis

(−0.375,−8.563)
left parenthesis negative 0.375 comma negative 8.563 right parenthesis

(0,−8)

Answer 1

To find the vertex of the quadratic equation \( y = 4x^2 + 3x - 8 \), we can use the vertex formula for a parabola given by the equation \( y = ax^2 + bx + c \). The x-coordinate of the vertex is calculated using the formula:

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

In this case:
- \( a = 4 \)
- \( b = 3 \)
- \( c = -8 \)

Substituting the values of \( a \) and \( b \):

\[
x = -\frac{3}{2 \cdot 4} = -\frac{3}{8}
\]

Next, we need to calculate the y-coordinate by substituting \( x = -\frac{3}{8} \) back into the original equation:

\[
y = 4\left(-\frac{3}{8}\right)^2 + 3\left(-\frac{3}{8}\right) - 8
\]
\[
= 4 \cdot \frac{9}{64} - \frac{9}{8} - 8
\]
\[
= \frac{36}{64} - \frac{72}{64} - \frac{512}{64}
\]
\[
= \frac{36 - 72 - 512}{64}
\]
\[
= \frac{-548}{64} = -8.5625
\]

Thus, the vertex of the quadratic \( y = 4x^2 + 3x - 8 \) is approximately:

\[
\left(-0.375, -8.563\right)
\]

So, the correct response from the given options is:

\(\left(-0.375, -8.563\right)\)