Question
Graph the quadratic y=4x2+3x−8. What is the vertex of this quadratic?(1 point) Responses (−1.838,0) left parenthesis negative 1.838 comma 0 right parenthesis (0,−8) left parenthesis 0 comma negative 8 right parenthesis (1.088,0) left parenthesis 1.088 comma 0 right parenthesis (−0.375,−8.563)
Answers
Answered by
GPT-4o mini
To determine the vertex of the quadratic \( y = 4x^2 + 3x - 8 \), we can use the formula for the vertex of a parabola given by the equation \( y = ax^2 + bx + c \). The x-coordinate of the vertex is given by:
\[
x = -\frac{b}{2a}
\]
In this case, \( a = 4 \) and \( b = 3 \).
1. Calculate the x-coordinate of the vertex:
\[
x = -\frac{3}{2 \times 4} = -\frac{3}{8} = -0.375
\]
2. Now, 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 step-by-step:
\[
y = 4(0.140625) - 1.125 - 8
\]
\[
y = 0.5625 - 1.125 - 8
\]
\[
y = 0.5625 - 9.125
\]
\[
y = -8.5625
\]
So, the vertex of the quadratic \( y = 4x^2 + 3x - 8 \) is \( (-0.375, -8.5625) \).
Given the options, the closest response indicating the vertex is:
\[
(-0.375, -8.563)
\]
Thus, the vertex is \( (-0.375, -8.563) \).
\[
x = -\frac{b}{2a}
\]
In this case, \( a = 4 \) and \( b = 3 \).
1. Calculate the x-coordinate of the vertex:
\[
x = -\frac{3}{2 \times 4} = -\frac{3}{8} = -0.375
\]
2. Now, 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 step-by-step:
\[
y = 4(0.140625) - 1.125 - 8
\]
\[
y = 0.5625 - 1.125 - 8
\]
\[
y = 0.5625 - 9.125
\]
\[
y = -8.5625
\]
So, the vertex of the quadratic \( y = 4x^2 + 3x - 8 \) is \( (-0.375, -8.5625) \).
Given the options, the closest response indicating the vertex is:
\[
(-0.375, -8.563)
\]
Thus, the vertex is \( (-0.375, -8.563) \).