Question

Graph the quadratic y = 4x2 + 3x - 8. What is the vertex of this quadratic? (1 point)
• (-0.375, —8.563)
• (1.088, 0)
• (0, -8)
• (-1.838, 0)

Answer 1

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

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

where \( a = 4 \) and \( b = 3 \).

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

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

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

\[
y = 4(-0.375)^2 + 3(-0.375) - 8
\]
\[
y = 4(0.140625) - 1.125 - 8
\]
\[
y = 0.5625 - 1.125 - 8
\]
\[
y = 0.5625 - 9.125
\]
\[
y = -8.5625
\]

Thus, the vertex of the quadratic function \( y = 4x^2 + 3x - 8 \) is approximately \( (-0.375, -8.5625) \). The answer finishes rounding to a more appropriate representation.

The correct option for the vertex from your list is:

\[
(-0.375, -8.563)
\]

So, the vertex is: **(-0.375, -8.563)**.