Question

The following graph describes function 1 and the equation below it describes function 2:

Function 1

graph of function f of x equals negative x squared plus 8 multiplied by x minus 15

Function 2

f(x) = -x^2 + 4x + 1

Function ____ has the larger maximum.
(Put 1 or 2 in the blank space)

Answer 1

@study100 I'd be very appreciative of your assistance.

Answer 2

would you mind if I use some calculus to solve this?

Answer 3

Whatever helps me find the answer is great!

Answer 4

1st function equation: -x^2 + 8(x-15)
simplify:
-x^2 +8x-120
2nd equation: -x^2 + 4x+1

Taking derivative will find the highest point of the parabola, since the slope of the parabola at its maximum is 0, and the derivative will allow us to find that.

derivative of 1st fuction= -2x + 8
solve for 0 : -2x+8= 0
x= -4

2nd fucntion der. -2x+4 = 0 x= 2

Now that you have those max points, plug them back in and compare which one has the highest maximum of y.

Answer 5

Sorry, 1st function x = 4

Answer 6

It would be the first function. Right?

Answer 7

Seems to me that it's the 2nd function

Answer 8

Okay. Thank you sooo much!

Answer 9

The following graph shows the functions f(x) and g(x):

graph of function f of x equals x squared and graph of function g of x equals x squared plus 3

The function g(x) is obtained by adding _______ to f(x). (only input integers)

Numerical Answers Expected!

Answer 10

isnt it 3??

Answer 11

f(x) = x^2
g(x) = x^2+3
Ans: 3
Yes :) <33

Answer 12

The function f(x) = -x2 - 7x + 30 shows the relationship between the vertical distance of a diver from a pool's surface f(x), in feet, and the horizontal distance x, in feet, of a diver from the diving board. What is a zero of f(x) and what does it represent?

x = 10; the diver hits the water 10 feet away horizontally from the board

x = 3; the diver hits the water 3 feet away horizontally from the board

x = 10; the diver jumps in the pool at 10 feet per second

x = 3; the diver jumps in the pool at 3 feet per second

@study100

Answer 13

f(x) = -x^2 -7x+ 30
f(x) = -(x+10)(x-3)
x= -10, 3 so you can eliminate A and C. Since it says that x is the horizontal distance from the board, answer B is the most correct response.

Answer 14

Thanks!!

Answer 15

using differentiation,

For function 1,
f(x)=-x^2+8x-15
f'(x)=-2x+8=0 for max
x=4
f(4)=1

for function 2,
f(x)=-x^2+4x+1
f'(x)=-2x+4=0 for max
x=2
f(2)=5

so function 2 have higher max value

Answer 16

Thanks @neoh147

Answer 17

welcome @BassCatcher15