Can someone help me with these equations ?

Question

Explain how a graph of quadratic function (f(x) = ax2 + bx + c) varies when the a,b,c changes from -1 to +1

Explain Product Rule, Quotient Rule and Power Rule

State the domain and range of the following relation: {(2,4), (-1,8), (4,-2), (5,6), (2,-2)} and State whether the relation is a function

Write the following logarithmic equations in exponential form

Log6 (√6) = ½

Log3 (9) = 2

Write the following exponential equations in logarithmic form.

5^2=25

10^-4=1/10,000

Solve the below:

(a) Find the inverse of f (x) = x^2. Then find the min and max given that -1<=x<1

(b) Calculate the area of a polygon if apothem = 5 and perimeter is 6.

(c) Given the slope m and "y intercept" b define the equation of this straight line.

(d) Explain the types of statistics 'measures of central tendency' and 'measures of dispersion and probability'

Solve the following inequality

x^2 + x – 2 > 0

Answer 1

Please just ask one question at a time. It will be difficult to answer the questions in a way that you will be able to learn from while keeping this answer to a readable length.

1.) "...graph of ax²+bx+c varies...": As a varies from -1 the graph varies from downward facing to upward facing. Varying b and c moves the graph left to right and down to up respectively (Rewrite the equation as "a(x-b/2a)²+c+-(b/2a)²=y" to understand this better)

2.) This is calculus, not algebra, and it basically asking if you have read some basic theorems. These theorems are that d/dx(AB) = dA/dx B +A dB/dx, d/dx(A/B) = (dA/dx B - A d/B/dx)/(B²), and d/dx (x^n) = n x ^(n-1). These can be rederived quickly from remembering the definition of a derivative.

3.) Inverse of x² is not a function. If you tried to apply this as a function to 2, you could either get an answer of 4 or -2. A function has to have exactly one output to each input. Domain is {-1,2,4,5}, range is {-2,4,6,8}.

4.), 5.) I'm not writing all of these as they are all variations of this basic idea: log_ba = c if and only if b^c=a

6.)i.) Inverse of x2 is not a function, as for example (-2)2=22=4. Inverse as a rule of y=x2 is ±|√y| for y≥0. x2 is a downward facing parabola, its min is at its vertex (0,0) and its maximums are at (-1,1) and (1,1) for domain -1≤x≤1

7.)ii.) Apothem for a polygon is distance from center to a side. Knowing that you can break up any polygon into triangles, each one having one of the sides as a base and apothem as height. Therefore summing together the areas and using the distributive law, total area would be one half apothem times perimeter, or 15

7.) iii.) It's y=mx+b. When x=0, y=b. When x=1, y=1+b, meaning we have risen height m from the x-intercept as we have run 1.

7.) iv.) First concept is what to consider the central value of a sample (mean median or mode) and second is how to consider how close the value are to the center (usually standard deviation)