Quadratics

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**Parabola** is the name of the shape the quadratic function makes. It looks a lot like a 'U'. // This is a Parabola. //
 * Quadratic Functions **


 * Maximum Value **- This is the highest y value in a quadratic function. This cannot happen in a regular Parabola, only flipped.
 * Minimum Value **- This is the lowest y value on the Parabola. In the picture above, it is the bottom of the 'U' and can only happen in a regular Parabola.
 * Vertex **- The middle of the highest/lowest point.
 * Axis of Symmetry **-The very center line going through the vertex
 * Zeroes, Roots, x-intercepts **- "Zeroes" refer to the x-intercepts of a graph, "roots" refer to the solution of an equation in the form p(x)=0.

Quadratic formula Graphing Factoring Taking the square root Completing the Square.
 * Methods for solving Quadratic equations: **

Vertex Form y=a(x-h) 2 +k Standard Form y=ax 2 +bx+c Intercept Form y=a(x-p)(x-q) (This is also called Factor Form) It is easy to transfer from form to form, so don't be afraid to. Standard form is the easiest to transfer to. When you solve using Intercept form, you can use the Zero Product Property (ZPP). Generally, when solving in Standard form, you should use the Quadratic Formula (seen below). // This property states that if (x)(y) is 0, then either x or y or both has to be 0. // Lets say we have 0=(x+1)(x-4) so we can assume that either x+1 or x-4 is 0. Using this knowledge we can infer that x is either 4 or -1. This means that our two solutions are x=-1 and x=4, or (4,0) and (-1,0) in point form. // ﻿ Since we put 0 in for y, or f(x), we can use this property to solve equations in intercept form with F(x)=(b)(c) as the basic format. So instead of f(x)=(b)(c) it would be 0=(b)(c). You always put the 0 in place of the variable that is by itself. // This formula is used to solve quadratics in standard form. ......-b__+__(sqrt)b 2 -4ac x= - ..............2a The discriminant (b 2 -4ac) indicates how many zeroes the parabola has.
 * 3 Forms of quadratic functions: **
 * Zero Product Property **
 * Quadratic Formula **

// What multiplies to be AC and adds to be B? // If we have x 2 +7x+10, we look at the factors of 7 and 10. What multiplies to be 10 and adds to be 7? The answer is 2 and 5. We then check using either the lattice method or the foil method by placing 2 and 5 into (x+n)(x+n) like (x+2)(x+5) x 2 +7x+10 quantity, therefore, 2,5 is correct. You can solve most quadratic equations by factoring depending on what form they are in (standard being the best). Checking is also very important, you should do it every time so you are 100% sure it is correct, it is very easy to make mistakes. You can factor things like 4x 3 -44x 2 +96x. To do this, you need to find the Greatest Common Factor (GCF). Variables can be GCFs', in this case, 4x is our GCF. We divide everything by 4x. 4x 2 -11x+24 is what we are left with. Then we just factor. 4x(x-8)(x-3) is what we should end up with.
 * Factoring **

If you have 5x 2 -6x+1, you have to multiply the +1 by 5, which would leave you with +5 at the end. Once this is done, just factor it normally. (X-1) (x-5) should be what we get. It won't always look like the above example, but you always multiply C and A, in this case it was 5(1).include component="comments" page="Quadratics" limit="4"