Given the parent functions f(x) = x, the function g(x) = -(x + 7)2 - 8 is
the result of shifts in the graph of Ax).
a. Describe the shift that takes fy) to g(x)
b. State the vertex of f(x)
c. State the axis of symmetry of g(x)

Step-by-step explanation:

Parent function f(x) = x²

a. Parent function f(x) when inverted about x- axis it becomes,

f'(x) = -x²

further f'(x) when shifted left by 7 units,

f"(x) = -(x + 7)²

followed by a shift of 8 units downwards forms,

g(x) = -(x + 7)² - 8

b. When we compare the function with vertex form of the quadratic function h(x) = -(x - h)² + k

Vertex of the transformed function g(x) will be (-7, -8)

c. Axis of symmetry of the function g(x) will be x = -7.

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step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.