Question

Graph the quadratic y=4x^2+3x−8 . What is the vertex of this quadratic?
Responses

(0,−8)

(−0.375,−8.563)

(−1.838,0)

(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 equation in the form \( y = ax^2 + bx + c \) is given by the formula:

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

In this equation, \( a = 4 \) and \( b = 3 \). Plugging in these values:

\[
x = -\frac{3}{2(4)} = -\frac{3}{8} \approx -0.375
\]

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

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

Calculating step by step:

1. \( (-0.375)^2 = 0.140625 \)
2. \( 4 \times 0.140625 = 0.5625 \)
3. \( 3 \times (-0.375) = -1.125 \)
4. Now substitute these values into the equation:
\[
y = 0.5625 - 1.125 - 8 = 0.5625 - 1.125 - 8 = -8.5625
\]

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

\[
(-0.375, -8.563)
\]

So the answer is:

**(−0.375,−8.563)**