Question

Graph the quadratic equation y=4x^2+3x-8. What is the vertex of this quadratic equation?
a. (1.088, 0)
b. (0, -8)
c. (-1.838, 0)
d. (-0.375, -8.563)

Answer 1

To find the vertex of the quadratic equation \( y = 4x^2 + 3x - 8 \), we can use the formula for the x-coordinate of the vertex, which is given by:

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

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

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

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

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

Calculating this step by step:

1. Calculate \( (-0.375)^2 \):
\[
(-0.375)^2 = 0.140625
\]

2. Now substitute this value:
\[
y = 4(0.140625) + 3(-0.375) - 8
\]

3. Calculate \( 4(0.140625) \):
\[
4 \cdot 0.140625 = 0.5625
\]

4. Calculate \( 3(-0.375) \):
\[
3 \cdot -0.375 = -1.125
\]

5. Now, sum them all up:
\[
y = 0.5625 - 1.125 - 8
\]
\[
y = 0.5625 - 1.125 = -0.5625
\]
\[
y = -0.5625 - 8 = -8.5625
\]

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

\[
(-0.375, -8.5625)
\]

Now, looking at the answer options you provided, the closest one appears to be:

**d. (-0.375, -8.563)**