Answer:
Part 1)
Part 2)
Part 3)
Part 4)
Part 5)
see the attached figure
Step-by-step explanation:
Solve each quadratic equation
Part 1) we have

Adds 32 both sides

Divide by 2 both sides

take square root both sides

therefore
The solutions are (-4,4)
Part 2) we have

Adds 100 both sides

Divide by 4 both sides

take square root both sides

therefore
The solutions are (-5,5)
Part 3) we have

Adds 55 both sides


take square root both sides

therefore
The solutions are (-8,8)
Part 4) we have

Adds 140 both sides

take square root both sides

therefore
The solutions are (-11,11)
Part 5) we have

Adds 18 both sides

Divide by 2 both sides

take square root both sides

therefore
The solutions are (-3,3)
Answer: x = -5, x = 6
<u>Step-by-step explanation:</u>
"Solutions" are also called roots, zeroes, and x-intercepts and are where the parabola crosses the x-axis.
The parabola crosses the x-axis at x = -5 and at x = 6
(see attachment)
<span>4x-2y=-1
</span><span>Slope = 2
x-intercept = -1/4
y-intercept = 1/2
</span><span>-4x+4y=-2
</span><span>Slope = 1
x-intercept = 1/2
y-intercept = 1/-2 </span>
So, this creates a triangle once again. If we imagine a slide, the slide itself would be the hypotenuse of the triangle, then if there's a ladder leading up to the slide, that would be the vertical length we're looking for. The feet across the ground would be the distance from the bottom of the slide to the bottom of the ladder.
We can use the Pythagorean theorem to find the missing side length, as this would create a right triangle. | 8^2 + b^2 = 10^2 | 64 + b^2 = 100 | b^2 = 36 | b = 6 feet | The slide is 6 feet high at its highest point.
Given the function:

Let's find the amplitude and period of the function.
Apply the general cosine function:

Where A is the amplitude.
Comparing both functions, we have:
A = 1
b = 4
Hence, we have:
Amplitude, A = 1
To find the period, we have:

Therefore, the period is = π/2
The graph of the function is shown below:
The parent function of the given function is:

Let's describe the transformation..
Apply the transformation rules for function.
We have:
The transformation that occured from f(x) = cosx to g(x) = cos4x using the rules of transformation can be said to be a horizontal compression.
ANSWER:
Amplitude = 1
Period = π/2
Transformation = horizontal compression.