Question

Graph the quadratic y=4x^2+3x−8 . What is the vertex of this quadratic?(1 point)
Responses

(0,−8)
left parenthesis 0 comma negative 8 right parenthesis

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

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

(−1.838,0)

Answer 1

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

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

In this case, \( a = 4 \) and \( b = 3 \).

Substituting these values into the formula:

\[
x = -\frac{3}{2 \cdot 4} = -\frac{3}{8} = -0.375
\]

Next, we find the y-coordinate of the vertex by substituting \( x \) back into the original equation:

\[
y = 4(-0.375)^2 + 3(-0.375) - 8
\]

Calculating \( (-0.375)^2 \):

\[
(-0.375)^2 = 0.140625
\]

Now substitute back:

\[
y = 4(0.140625) + 3(-0.375) - 8
\]
\[
y = 0.5625 - 1.125 - 8
\]
\[
y = 0.5625 - 9.125
\]
\[
y \approx -8.5625
\]

Thus, the vertex is approximately \( (-0.375, -8.563) \).

So, the correct response is:

\[
\text{(−0.375,−8.563)}
\]