Quadratics

A is like m. A is the rate of change of how much the parabola changes.

A is the same across all forms.

Standard Form: To find y-intercept: y=ax2+bx+c       c=y-intercept

Vertex Form: To find vertex             y=a(x-h)2+k      (h,k)=vertex coordinates

Factored: To find x-intercepts          y=a(x+r1)(x+r2) or y=(x+a)(x+b)  (r1,0) & (r2,0)= x-intercepts '''a: if positive, it opens up. a<1= vertical compression, a>1= vertical stretch'''

Reflections-Across x-axis: -f(x) Flip the signs of a, b and c

Across y-axis: f(-x)

Flip the x sign

If in parenthesis, switch the signs/multiply by -1.

Ex: x of vertex is h times -1, x-intercepts are r1 times -1 and r2 times -1

r=radius (imagine a circle where the point is on the perimeter and the origin is the center)

Vertex to standard- FOIL the parenthesis and add k

Standard to vertex- Find the x and y of the vertex and replace h with the x and k with the y. You could also complete the square.

Standard to Factored: Factor or do quadratic formula

Factored to Standard: FOIL the parenthesis

Factored to Vertex: Convert to standard, then to vertex

Vertex to factored: Convert to standard, then to factored form

Domain: -(infinity) < x < (infinity)

Range: y ≥/≤ (y of vertex)

Axis of symmetry= Average of x-intercepts`