University:
York University
Course:
MATH 1013 | Applied Calculus
Academic year:

2023
Views:

231

Pages:

2
Author:

Niklas

I. Polynomials QUADRATIC FUNCTIONS (Ch. 2-1) I. QUADRATICS: parent function: (f(x)=x^{2}) analyzing the parent function: [f(x)] x-int: {0} X -2 4 y-int O -1 vertex: (V(0,0)) 0 0 axis of symmetry: (x=0) domain: D(-00,00) 2 4 range: R: [0,00) axis of symmetry line over which the parabola is symmetric. vertex point where the parabola intersects the axis 1. find the equation of a line that is transformed 4 left, 2 up, and reflects about the x-akis. \(f(x)=-(x+4)^{2}+2\) 2. graph the following: \(f(x)=-(x-2)^{2}+4\) domain: (D:(-\infty,\infty)) [\underline{f(x)}] range: [R(\cdot\infty,4]] X -1 50343 vertex: [\underline{V(2,4)}] 0 roots [{0,4}] 1 axis of symmetry (\underline{x+2}) 2 yint 3 4 5-5 forms of the quadratic equation → vertex form vertex (n,k) [f(x)=a(x-h)^{2}+k] axis: (x=h) → standard form [(\frac{-b}{2a},-\frac{b^{2}-4ac}{4a})] f(x)= (ax^{2}+bx+c) axis: (x=\frac{-b}{2a}) II COMPLETING THE SQUARE convert from standard form to vertex form •Let ax^2+bx+c=0 for a=1 i. group the x^2 and x terms together as long as quadratic is set equal to 0. (x^2+bx)+c=0 ii. add and subtract b^2/4 (x^2+bx+b^2/4)+c-b^2/4=0 iii. factor the perfect square trinomial and combine the constants. (x)=-VERTEX FORM .(h an og x^2+8y=10) to vertex form. (x^2+8x)-10=0 (x+8x+16)-26-0 (x+4)^2-26=D Change x^2+16x-9=0 to vertex form. (x^2+16x)-9=0 (x^2+16x+64)-73=0 (x+8)^2-13*0 let ax^2bx+c0. for a=1: i. force factor out a. a(y^2+b/a*x+c/a) ii. add and subtract b^2/4a^4 to the group. Q((x^2+b/ax+b^2/44a^2)+c/ab^2/44a^2) iii. factor the perfect square trinomial and combine the constants. a((y+b/2a)^2-b^2-4ac/4a^2) iv. distribute a. a(x+b/2a)^2-b^2-4ac/4a -VERTEX FORM