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Graphing inequalities with calculator to find the maximum earnings of two part-time jobs

Q: Anna is a college student with two part-time jobs, one at a hardware store and the other at a fitness centre. She wants to work a minimum of 7 h/week at the hardware store, and 5h/week at the fitness centre . She does not want to work more than 15 h/ week. the . . . → Read More: Graphing inequalities with calculator to find the maximum earnings of two part-time jobs

What is a Parabola?

Q: What are parabolas?

A: Parabolas are conic sections. The standard form is

The vertex is located at (p,q)

♦  Note that (x-p) means that the x-coordinate of the vertex is p ♦  Conversely, (x+p) means that the x-coordinate of the vertex is at -p

a is the ‘slope’ of the parabola, determining . . . → Read More: What is a Parabola?

Graphing a Parabola

Q: What if I don’t have an Equation Solver, how do I graph a parabola?

A: The easiest way is to make a table of values. To keep things simple, let’s look again at . To generate a table of values, simply substitute different values of x to obtain the corresponding value of y. . . . → Read More: Graphing a Parabola

Positive and Negative Parabolas

Q: What is the difference between a positive and a negative parabola?

A: The sign (+ or -) of the a value determines if the parabola opens upwards or downwards.

Let’s compare the graphs of , where a=+1 and , where a=-1. . . . → Read More: Positive and Negative Parabolas

Changing the value of a in Parabola equation y=a(x-p)^2+q

Q: What happens if I change the value of a?

A: This affects the steepness or ‘slope’ of the parabola.

Let’s compare 3 graphs with different a values: a=2, a=1, and a=0.5

Changing the value of p in Parabola equation y=a(x-p)^2+q

Q: What happens if I change the value of p?

A: p is the x-coordinate of your vertex. If it changes, the parabola will shift left or right.

Note that the general equation for a parabola is

(x-p) means:

if you have a positive p value, the result will be (x-p) if you . . . → Read More: Changing the value of p in Parabola equation y=a(x-p)^2+q

A Farmer Wants to Maximize Area

Q: A farmer wants to put a fence around a vegetable garden. Only three sides must be fenced, since a rock wall will form the fourth side. If he uses 40m of fencing what is the maximum area possible?

A:  Okay, so we have two widths and one length.

The material used would . . . → Read More: A Farmer Wants to Maximize Area

Introduction to Algebra

Algebra is the basis for much of the math taught in high school. Too often, grade 11 or 12 students struggle with simple algebra that they should have mastered in grade 8. Improving your algebra skills is extremely important if you want to succeed in high school and university.

As a general rule, any . . . → Read More: Introduction to Algebra

Max/Min Problem, Difference of Two numbers

Q: Two numbers hava a difference of 16. Find the numbers if their product is a minimum.

A: Let x = first number Let y = second number

Equation 1: x-y = 16 Equation 2: xy=P , where P is the product.

You need to isolate for x or y in Equation 1, and . . . → Read More: Max/Min Problem, Difference of Two numbers

Math 11: A Rectangle Word Problem using the Quadratic Formula

Formula for perimeter of a rectangle: P = 2w + 2l, where w=width and l=length

Formula for area of a rectangle: A = wl

30 = 2w+2l

40 =wl

In the area formula, isolate for l:

l = 40/w

Substitute this into the perimeter formula:

30 = 2w + 2(40/w) 30 = 2w + . . . → Read More: Math 11: A Rectangle Word Problem using the Quadratic Formula