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kohat485
22.07.2019 •
Mathematics
Use these functions to answer the questions. f(x)=(x+3)^2−1 g(x)=−2x^2+8x+3 h(t)=−16t^2+28t part a what are the x- and y-intercepts of the graph of the function f(x)? identify the coordinates of any maxima or minima of the function. explain your answers. part b write the function g(x) in the form y=a(x−h)2+k . write the equation for the line of symmetry for the graph of g(x). show all your work and explain your answer. part c the function h(t) gives the approximate height, in feet, of a dolphin's jump out of water, where t represents the time, in seconds. what is the total length of time, in seconds, it took the dolphin to complete one jump? show your work.
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Ответ:
B) Vertex form is g(x) = -2(x-2)²+11, and the axis of symmetry is at x=2.
C) It takes 1.75 seconds for the dolphin to complete one jump.
Explanation:
A) To find the x-intercepts, we replace y (in this case, f(x)) with 0 and solve:
0 = (x+3)²-1
First, add 1 to both sides:
0+1 = (x+3)²-1+1
1 = (x+3)²
Take the square root of both sides:
√1 = √(x+3)²
+/- 1 = x+3
Subtract 3 from both sides:
-3 +/- 1 = x
This means x=-3-1 and x=-3+1, or x=-4 and x=-2.
B) To write g(x) in vertex form, we must complete the square. First we will factor the GCF of the first two terms out:
g(x) = -2(x²-4x)+3
To find the value that we add (and subtract, to maintain equality) to this function, we take half of the value of b (the one in parentheses) and square it:
(-4/2)²=(-2)²=4
This is what we will add in parentheses. Since this will be multiplied by -2, this means to cancel it, we will add 8 as well (2*-4 = -8; -8+8=0):
g(x)=-2(x²-4x+4)+3+8
g(x)=-2(x²-4x+4)+11
Factoring the trinomial in parentheses, we have
g(x) = -2(x-2)²+11.
The axis of symmetry is given by x = -b/2a:
x = -8/2(-2) = -8/-4 = 2
C) We will set this equal to 0 to solve it:
0 = -16t² + 28t
Now we will factor out the GCF, 4t:
0 = 4t(-4t+7)
Using the zero product property, we know that either 4t=0 or -4t+7=0:
4t=0
Divide both sides by 4:
4t/4 = 0/4
t = 0
This is when the dolphin first jumps.
-4t+7=0
Subtract 7 from both sides:
-4t+7-7=0-7
-4t = -7
Divide both sides by -4:
-4t/-4 = -7/-4
t = 7/4 = 1.75
Ответ:
the answer is A.5 B.9 C.32 hope this helps!!
Step-by-step explanation: