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 (−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

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 can be calculated using the formula:

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

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

Substituting these values into the formula, we have:

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

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

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

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

\[
4(0.140625) = 0.5625
\]

Calculating \( 3(-0.375) \):

\[
3(-0.375) = -1.125
\]

Now we can put it all together:

\[
y = 0.5625 - 1.125 - 8
\]

Calculating \( 0.5625 - 1.125 = -0.5625 \), then:

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

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

\[
(-0.375, -8.5625)
\]

Thus, the closest response for the vertex of the quadratic is:

\[
\text{(−0.375,−8.563)}
\]