Introduction to Quadratics

​ Introduction to Quadratics

​ Transformation equations

​Standard Form	​Vertex Form
​y = ax2 + bx + c	​y = a(x - h)2 + k
​f(x) = ax2 + bx + c	​f(x) = a(x - h)2 + k

​ Parent function y = x²

Graph of parent function

• parabola

• vertex at origin

• opens up

​Parts of the function we will be graphing

• vertex

• axis of symmetry

• x-intercepts

• y-intercept

• domain

• range

​Types of graphs you might see

​Finding the y-intercept in standard form
let x = 0

​y = ax² + bx + c

y = a(0)² + b(0) + c

y = 0 + 0 + c

y = c

Therefore y-intercept = (0, c)

​Finding the x-intercept in Standard Form let y = 0

• Factoring

  • Zero Product Rule

• Quadratic Formula

• Completing the Square

  • y = a(x - h)² + k

​Possible x-intercepts
aka..... (roots, solution, zeros)


Since quadratic are x² the "2" in the exponent tells you it will always have 2 answers

Although the answer could be

• 2 distinct answers

• multiple root (same answer appears twice)

• 2 imaginary root

​Axis of Symmetry

• Will always go through the VERTEX (h, k)

• Will always be a vertical line

• Will always be x = h

​Finding the y-intercept in Vertex Form
let x = 0

y = a(x - h)² + k
y = a(0 - h)² + k
y = ah² + k

​Finding the x-intercept in Vertex form
let y = 0

​ y = a(x - h)² + k

• square root method

• Put in standard form and use standard form method

​If all else fails...........
make a T- table and substitute number


y = x² + 3x + 2

​x	x2 + 3x + 2	​y
​-2	​ (-2)2 + 3(-2) + 2 = 0	​0
​-1	​ (-1)2 + 3(-1) + 2 = 0	​0
​0	​ (0)2 + 3(0) + 2 = 2	​2
​1	​ (1)2 + 3(1) + 2 = 6	6​
​2	​(2)2 + 3(2) + 2 = 0	​12

​Rules when making a T-table
1) must use at least 5 point

2) must have at least 2
y-values that repeat