Graph the quadratic y=4x^2+3x−8

Question

. What is the vertex of this quadratic?(1 point)
Responses

(0,−8)
left parenthesis 0 comma negative 8 right parenthesis

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

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

(1.088,0)

Answer 1

To find the vertex of the quadratic equation \(y = 4x^2 + 3x - 8\), we can use the vertex formula for a parabola given in standard 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 \(b = 3\).

1. Calculate the x-coordinate of the vertex: \[ x = -\frac{3}{2(4)} = -\frac{3}{8} = -0.375 \]

2. Now substitute \(x = -0.375\) back into the equation to find the y-coordinate:

   \[ y = 4(-0.375)^2 + 3(-0.375) - 8 \] \[ = 4(0.140625) - 1.125 - 8 \] \[ = 0.5625 - 1.125 - 8 \] \[ = 0.5625 - 9.125 = -8.5625 \approx -8.563 \]

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

\[ (-0.375, -8.563) \]

So, the correct response is:

(−0.375,−8.563)