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Quadratic Equation Forms Guide

This document provides an overview of the key forms of quadratic equations and how to transition between them. It shows the standard, factored, and vertex forms of quadratics along with the key points and transformations needed to go between the forms. The standard steps include expanding, factoring, completing the square, finding the vertex, roots, intercepts, and converting between equivalent equations.

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Elaine zhu
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77 views1 page

Quadratic Equation Forms Guide

This document provides an overview of the key forms of quadratic equations and how to transition between them. It shows the standard, factored, and vertex forms of quadratics along with the key points and transformations needed to go between the forms. The standard steps include expanding, factoring, completing the square, finding the vertex, roots, intercepts, and converting between equivalent equations.

Uploaded by

Elaine zhu
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Finding Your Way Around Quadratic Equations

Form Equation Example

Factored f(x) = a(x – s)(x – r) f(x) = 2(x – 3)(x + 5)


Equivalent
Standard f(x) = ax2 + bx + c f(x) = 2x2 + 4x – 30 Equations
Vertex f(x) = a(x – h)2 + k f(x) = 2(x + 1)2 – 32

Change
Given Key Points Action Example Method
to…
x-intercepts/ Take s and r
x-intercepts = (3,0)
solutions/ from the Expand:
and (-5,0) Standard f(x) = 2(x – 3)(x + 5)
roots equation
Form f(x) = 2(x2 + 2x -15)
f(0) = 2(0 – 3)(0 + 5) f(x) = 2x2 + 4x - 30
y-intercept Find f(0)
f(0) = -30
Factored Form
f(x) = 2(x – 3)(x + 5) AOS
Find vertex and sub for
Find AOS and x = (s + r)/2
h and k equation. Keep
sub into = (3 – 5)/2 Vertex
vertex a-value:
original = -1 Form
equation f(-1) = -32
f(x) = 2(x + 1)2 – 32
vertex = (-1, -32)

x-intercepts/ Factor or use ac/product = -15


solutions/ quadratic b/sum = 2 Factor:
roots formula f(x) = 2(x – 3)(x + 5) Factored ac/product = -15
Form b/sum = 2
“c” is the y- f(x) = 2(x – 3)(x + 5)
Standard Form y-intercept (0, c) = (0, -30)
intercept
f(x) = 2x2 + 4x - 30
Use x = -b/2a Find vertex and sub for
x = -4/[(2)(2)]
to find vertex h and k equation. Keep
x = -1 Vertex
vertex and sub into a-value:
f(-1) = -32 Form
original
vertex = (-1, -32)
equation f(x) = 2(x + 1)2 – 32

0 = 2(x + 1)2 – 32
x-intercepts/ 32 = 2(x + 1)2
Set equation Find roots and sub into
solutions/ 16 = (x + 1)2
equal to zero factored form. Keep
roots ±4 = x + 1 Factored
a-value:
x = 3 and -5 Form
Vertex Form
f(x) = 2(x – 3)(x + 5)
f(x) = 2(x + 1)2 – 32 f(0) = 2(0 + 1)2 – 32
y-intercept Find f(0)
f(0) = -30

From the Expand:


Standard
vertex equation vertex = (-1, -32) f(x) = 2(x+1)(x+1) – 32
Form
vertex = (h, k) f(x) = 2x2 + 4x - 30

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