Respuesta :
Answer:
Below in bold.
Step-by-step explanation:
A. −16x2 + 24x + 16 = 0
-8(2x2 - 3x - 2) = 0
-8(2x + 1 )(x - 2) = 0
x = -0.5, 2.
So the x-intercepts are (-0/5, 0) and (2, 0).
B. As the leading coefficients is negative (-16) the vertex of the graph will be a Maximum.
To find its coordinates we convert the function to vertex form:
f(x) = −16x2 + 24x + 16
= -16(x^2 - 1.5x) + 16
Completing the square on contents of the parentheses:
= -16 [(x - 0.75)^2 - 0.75^2] + 16
= -16(x - 0.75)^2 - 16 * -0.75^2 + 16
= -16(x - 0.75)^2 + 9 + 16
= -16(x - 0.75)^2 + 25.
So the coordinates of the vertex are (0.75, 25)
x-intercepts are (-1/2, 0), (2, 0) and coordinates of the vertex are (3/4, 25).
The given function is f(x)=-16x²+24x+16.
How to find x-intercept?
To find the x-intercept we set y = 0 and solve the equation for x.
Part A: To find the x-intercept, substitute 0 for y and solve for x.
To find the y-intercept, substitute 0 for x and solve for y.
x-intercepts: (-1/2, 0), (2, 0)y-intercepts: (0, 16)
Part B: Use the formula x=-b/2a to find the maximum and minimum. (3/4, 25)
Rewrite in vertex form and use this form to find the vertex (h, k).
(3/4, 25)
Part C: The parabola uses the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex: (3/4, 25)
Focus: (3/4, 1599/64)
Axis of symmetry: x=3/4
Directrix: y=1601/64
Coordinates to plot the graph is (0, 16), (3/4, 25) and (2, 0).
Therefore, x-intercepts are (-1/2, 0), (2, 0) and coordinates of the vertex are (3/4, 25).
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