Question

Which of the following coordinate pairs is a point on the parabola y=2x^2−24x−15 ?
(2,−15) left parenthesis 2 comma negative 15 right parenthesis (−11,7) left parenthesis negative 11 comma negative 7 right parenthesis (2,−47) left parenthesis 2 comma negative 47 right parenthesis (11,−37)

Answer 1

Determine the zero(s) of the quadratic function y=2x^2+9x+4 .
There are no zeros. There are no zeros. (0,4) left parenthesis 0 comma 4 right parenthesis (−4,0)(−0.5,0) left parenthesis negative 4 comma 0 right parenthesis left parenthesis negative 0.5 comma 0 right parenthesis (4,0)(−1,0)

Answer 2

Identify the vertex of y=−2(x−13)^2+47 .
(13,47) left parenthesis 13 comma 47 right parenthesis (26,47) left parenthesis 26 comma 47 right parenthesis (−13,47) left parenthesis negative 13 comma 47 right parenthesis (−2,47)

Answer 3

To determine if a coordinate pair is on the parabola, we can substitute the x and y values into the equation and see if both sides of the equation are equal.

For the first coordinate pair (2, -15):
Substituting x = 2 and y = -15 into the equation y = 2x^2 - 24x - 15:
-15 = 2(2)^2 - 24(2) - 15
-15 = 8 - 48 - 15
-15 = -55

Since -15 is not equal to -55, the point (2, -15) is not on the parabola.

Similarly, we can check the other coordinate pairs:
For (−11, 7):
7 = 2(-11)^2 - 24(-11) - 15
7 = 2(121) + 264 - 15
7 = 242 + 264 - 15
7 = 491

Since 7 is not equal to 491, the point (−11, 7) is not on the parabola.

For (2, -47):
-47 = 2(2)^2 - 24(2) - 15
-47 = 8 - 48 - 15
-47 = -55

Since -47 is not equal to -55, the point (2, -47) is not on the parabola.

For (11, -37):
-37 = 2(11)^2 - 24(11) - 15
-37 = 2(121) + 264 - 15
-37 = 242 + 264 - 15
-37 = 491 - 15
-37 = 476

Since -37 is not equal to 476, the point (11, -37) is not on the parabola.

Therefore, none of the given coordinate pairs are points on the parabola y = 2x^2 - 24x - 15.

Answer 4

To determine the zero(s) of a quadratic function, we need to find the x-values where the function equals zero. In other words, we need to solve the equation 2x^2 + 9x + 4 = 0.

This can be done by factoring, completing the square, or using the quadratic formula.

Since the quadratic equation does not factor easily, we will use the quadratic formula:

Given the quadratic equation ax^2 + bx + c = 0, the quadratic formula is:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = 9, and c = 4.

Plugging these values into the quadratic formula, we have:

x = (-9 ± √(9^2 - 4(2)(4))) / (2(2))

Simplifying further:

x = (-9 ± √(81 - 32)) / 4

x = (-9 ± √49) / 4

x = (-9 ± 7) / 4

Solving for both possibilities:

x = (-9 + 7) / 4 = -2/4 = -0.5

x = (-9 - 7) / 4 = -16/4 = -4

Therefore, the zeros of the quadratic function y = 2x^2 + 9x + 4 are x = -0.5 and x = -4.

Answer 5

To identify the vertex of a quadratic function in the form y = a(x - h)^2 + k, the vertex is represented by the point (h, k).

In this case, the quadratic function is y = -2(x - 13)^2 + 47.

Comparing it to the general form, we see that the vertex has coordinates (h, k) = (13, 47).

Therefore, the vertex of the quadratic function y = -2(x - 13)^2 + 47 is (13, 47).