Question

2. Given the table of values, complete the table for the quadratic equation y = -6x² + 3x + 8 to find the values of the high or low point of the parabola.
x y
-1 -1
-.75 2.375
-.5 5
-.25
0 8
.25 8.375
.5
.75
1 5

Which of the following is correct?
• (-1,-1) is the low point of the parabola
• (.5,9) is the high point on the parabola
• (.25,8.375) is the high point on the parabola
• (.25,8.375) is the low point on the parabola

Answer 1

To find the high or low point of the parabola, we need to find the vertex of the quadratic equation. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c.

For the given equation y = -6x² + 3x + 8, a = -6 and b = 3.

x = -3/(2*(-6))
x = -3/(-12)
x = 1/4

Substituting x = 1/4 into the equation y = -6x² + 3x + 8, we can find the y-coordinate of the vertex.

y = -6(1/4)² + 3(1/4) + 8
y = -6(1/16) + 3/4 + 8
y = -3/8 + 3/4 + 8
y = -3/8 + 6/8 + 8
y = 5/8 + 8
y = 5/8 + 64/8
y = 69/8

So, the vertex is located at (1/4, 69/8) which is approximately (0.25, 8.625).

Therefore, the correct answer is: (.25,8.375) is the high point on the parabola.