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

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

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

(0,−8)

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 quadratic function \(y = ax^2 + bx + c\). The x-coordinate of the vertex is given by:

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

In this quadratic, \(a = 4\) and \(b = 3\). Plugging these values into the formula gives us:

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

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

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

Calculating \(4(-0.375)^2\):

\[
4 \cdot 0.140625 = 0.5625
\]

Calculating \(3(-0.375)\):

\[
-1.125
\]

Now putting it all together:

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

Thus, the vertex of the quadratic \(y = 4x^2 + 3x - 8\) is approximately \((-0.375, -8.563)\).

So, the correct response is:

\[
(-0.375, -8.563)
\]