Given the table of values, complete the table for the quadratic equation y = -6x^2 + 3x + 8 to find the values of the high or low point of the parabola.
The table:
x, y
-1 -1
-0.75 2.375
-0.5 5
-0.25
0 8
0.25 8.375
0.5
0.75
1 5
Which of the following is correct?
A. (0.25, 8.375) is the low point on the parabola.
B. (-1, -1) is the low point on the parabola.
C. (0.5, 9) is the high point on the parabola.
D. (0.25, 8.375) is the high point on the parabola.
To find the high or low point of the parabola, we need to find the vertex. The x-coordinate of the vertex can be found using the formula x = -b/2a. In this case, a = -6 and b = 3, so x = -3/(2*(-6)) = 0.25.
To find the y-coordinate of the vertex, we substitute the x-coordinate into the equation. Plugging in x = 0.25, we get y = -6(0.25)^2 + 3(0.25) + 8 = 8.375.
Therefore, the high or low point of the parabola is (0.25, 8.375).
The correct answer is:
D. (0.25, 8.375) is the high point on the parabola.
To find the values of the high or low points of the parabola, we need to determine the vertex. The vertex of a quadratic equation in the form y = ax^2 + bx + c can be found using the formula x = -b/2a.
In this case, the equation is y = -6x^2 + 3x + 8. So, a = -6, b = 3, and c = 8.
Substituting the values into the formula, we have:
x = -3 / (2 * -6)
x = -3 / -12
x = 0.25
To find the corresponding y-value (the value of y when x = 0.25), we substitute 0.25 into the equation:
y = -6(0.25^2) + 3(0.25) + 8
y = -6(0.0625) + 0.75 + 8
y = - 0.375 + 0.75 + 8
y = 8.375
So, the vertex of the parabola is (0.25, 8.375).
Based on the given table, we can see that the point (0.25, 8.375) is present, which confirms that it is indeed the high or low point. Therefore, the correct answer is:
D. (0.25, 8.375) is the high point on the parabola.
To find the values of the high or low point of the parabola, we need to complete the missing values in the table by substituting the given x-values into the quadratic equation y = -6x^2 + 3x + 8 and calculate the corresponding y-values.
Let's complete the table:
x, y
-1 -1
-0.75 2.375
-0.5 5
-0.25 ?
0 8
0.25 8.375
0.5 ?
0.75 ?
1 5
To find the value of y when x = -0.25, we substitute it into the equation:
y = -6(-0.25)^2 + 3(-0.25) + 8
y = -6(0.0625) - 0.75 + 8
y = -0.375 - 0.75 + 8
y = 7.875
Now we can fill in the missing values:
x, y
-1 -1
-0.75 2.375
-0.5 5
-0.25 7.875
0 8
0.25 8.375
0.5 ?
0.75 ?
1 5
To find the value of y when x = 0.5, we substitute it into the equation:
y = -6(0.5)^2 + 3(0.5) + 8
y = -6(0.25) + 1.5 + 8
y = -1.5 + 1.5 + 8
y = 8
To find the value of y when x = 0.75, we substitute it into the equation:
y = -6(0.75)^2 + 3(0.75) + 8
y = -6(0.5625) + 2.25 + 8
y = -3.375 + 2.25 + 8
y = 6.875
Now we have the completed table:
x, y
-1 -1
-0.75 2.375
-0.5 5
-0.25 7.875
0 8
0.25 8.375
0.5 8
0.75 6.875
1 5
To find the high or low point on the parabola, we need to look for the maximum or minimum value of y. By observing the completed table, we can see that the maximum y-value is 8.375, which occurs when x = 0.25. Therefore, the high point on the parabola is (0.25, 8.375).
Therefore, the correct answer is:
D. (0.25, 8.375) is the high point on the parabola.