Question

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

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

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

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

(1.088,0)

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 in the form \( ax^2 + bx + c \) can be found using the formula:

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

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

Substituting these values into the formula gives us:

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

Next, we substitute this x-value back into the original equation to find the y-coordinate of the vertex:

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

Calculating each term step-by-step:

1. Calculate \( (-0.375)^2 = 0.140625 \).
2. Calculate \( 4 \times 0.140625 = 0.5625 \).
3. Calculate \( 3 \times (-0.375) = -1.125 \).
4. Now substitute back into the equation:

\[
y = 0.5625 - 1.125 - 8 = 0.5625 - 1.125 = -0.5625 \quad \text{and then} \quad -0.5625 - 8 = -8.5625
\]

So the vertex is:

\[
(-0.375, -8.5625)
\]

Considering the available responses and rounding:

The approximate coordinates of the vertex are:

\((-0.375, -8.563)\).

Thus, the correct answer is:

**(−0.375,−8.563)**