Quadratics

Quadratic equations: Parabola

Quadratics

A formula is called a quadratic if it has the form

$y=\blue ax^2+\green bx+\purple c$ where $\blue a$ , $\green b$ , and $\purple c$ are numbers and $\blue a\ne0$ .

Example

$\begin{array}{rcl}y&=&\blue 3x^2\green{-2}x+\purple 3 \end{array}$

Reducing to standard form

Quadratics can be expressed in a number of different ways. By expanding the brackets, it becomes clear whether the formula is indeed a quadratic and what the values of $\blue a$ , $\green b$ , and $\purple c$ are.

Example

$\begin{array}{rcl}y&=&\left(2x+2\right)\left(x+3\right)\\ &=& 2x^2+x \cdot 2 +2x\cdot 3+2 \cdot 3 \\ &=& \blue 2x^2+\green 8x+\purple 6 \end {array}$

Take a look at the formula $y=-6\cdot x^2+36\cdot x-49$ .

Give the values of $a$ , $b$ , and $c$ when we write the formula in the form $y=ax^2+bx+c$ .

$a=$ $-6$
$b=$ $36$
$c=$ $-49$

When we compare $y=-6\cdot x^2+36\cdot x-49$ with $y=ax^2+bx+c$ , we find
$a=$ $-6$
$b=$ $36$
$c=$ $-49$

New example