Question

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

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

(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

(−1.838,0)

Answer 1

To find the vertex of the quadratic equation \( y = 4x^2 + 3x - 8 \), we can use the vertex formula \( x = -\frac{b}{2a} \), where \( a \) is the coefficient of \( x^2 \) and \( b \) is the coefficient of \( x \).

In this equation:
- \( a = 4 \)
- \( b = 3 \)

Now, we can calculate the \( x \)-coordinate of the vertex:

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

Next, we need to find the \( y \)-coordinate by substituting \( x = -0.375 \) back into the quadratic equation:

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

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

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

Now substituting this back in:

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

Thus, the vertex of the quadratic is:

\[
(-0.375, -8.5625)
\]

The closest match from your provided options is:

**(−0.375, −8.563)**

So the vertex of the quadratic is \((-0.375, -8.563)\).