Month: October 2018

Parabolic Graphing

The standard type of a quadratic equation is y=ax² + bx + c , where a, b, and c are real numbers, and that a can never equal 0. Each term in the condition has its own significance. The vertex of the parabola is its highest or lowest point. A determines the size of the parabola, b determines the x-int, and c determines the y-int. The vertex may be a minimum point or a maximum. If a is less than 0, than the vertex would be a maximum and the parabola would open downwards. If a is bigger than 0, than the vertex would be the minimum and the parabola would open upwards. The axis of symmetry is the line that runs vertically through the vertex, showing the starting point on a line when the parabola has moved away from the original graph lines. The domain would be all possibilities than run along the x-axis, the range would be all possibilities that run along the y-axis. The Parabola can be of different sizes and different directions(up or down), depending on the a value. 4x² would produce a more compressed parabola in the upwards direction, while 1/4x² would give a wider parabola.

Here is some help. https://www.youtube.com/watch?v=7QMoNY6FzvM

Discriminant

A discriminant is the part of the quadratic formula in the square root, which is (b² – 4ac). The complete quadratic formula is  The discrimant tells us how many solutions there are, aswell as what x means and its properties. It helps us to determine a shortened answer without going through mulyiple calculations, which only works in some situations. A positive discriminant means that the quadratic has two real number solutions. A discriminant of zero means that the quadratic has a one real number solution. A negative discriminant means that there are no solutions.

To start, lets start with x²+5x+6=0. In this case, a = 1, b = 5 and c = 6. When you plug them in the equation for finding the discriminant, it becomes 5² – 4(1)(6).

Then it becomes, 25 – 24

Then the asnwer is, 1, meaning there would be 2 answers.

For more info check out : https://www.purplemath.com/modules/quadform2.htm

Perfect square trinomials

Perfect trinomials are fairly easy to complete once you get the hang of simple tactics of quickly factoring/solving the equation. Perfect square trinomials are algebraic expressions/equations that are squared by the same binomial. As such, like any squared number, an easy way to identify one of its numbers/expressions is to square root the last number in the equation. Only do this if certain that it is a perfect square trinomial. eg. x² + 12x + 36. We would take the 36 and square root it, which makes 6. Then we would look at the first coefficient and see what the number is. Usually, the number is only 1 (x²), which means x was multiplied by itself once. then we form our factor. It would look like (x + 6).

Here is a link to a helpful video: 

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Simple Trinomials

A simple trinomial is a mathematic expression with 3 terms of different meanings and values. The usual expression has x as the variable but any letter can be put in its place. As trinomials get more complicated there can be multiple answers, but as for now, simple trinomials have just one. The answer to a simple trinomial should be in a fraction form: e.g (x+5)(x+3).

Here is a link to a helpful video: 

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A simple equation could be x²+6x+8

I usually do the “tic tac toe” method but for now, I will try and make it simple.

We first start with seeing products of the 8. We need to find a set of products that add to the middle number(6x).

We have 8,1 and  4,2.

4 and 2 seem to add up to 6. This means all we have to do is just to factor them. Just put both in brackets accompanied with an x.

(x+4)(x+2)