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

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

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

(1.088,0)

Answer 1

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

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

Here, \( a = 4 \) and \( b = 3 \).

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

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

Now, to find the y-coordinate of the vertex, we substitute \( x = -0.375 \) back into the quadratic equation:

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

Calculating this step-by-step:

1. Calculate \( (-0.375)^2 = 0.140625 \)
2. Multiply by 4: \( 4 \cdot 0.140625 = 0.5625 \)
3. Calculate \( 3 \cdot (-0.375) = -1.125 \)
4. Now, combine:

\[
y = 0.5625 - 1.125 - 8 = 0.5625 - 1.125 - 8 = -0.5625 - 8 = -8.5625
\]

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

\[
(-0.375, -8.5625)
\]

Since the option closest to this value in your responses is:

**(−0.375,−8.563)**

So the answer is:

**(−0.375,−8.563)**.