Graphing Quadratics
Graph the quadratic function
y=-2(x-1)^2+3
Vertex: (1,3) AOS x=1, yi(0,1) other point (2,1)
Write a Quadratic function in vertex form:
Vertex: (1,2) Other point: (3,10)
y=2(x-1)^2+2
What are all of the key features of a quadratic?
1. Y- intercept
2. X- intercepts
3. Vertex
4. AOS
5. Other Point
Rewrite the quadratic function f(x)=x^2+6x+8 in vertex form.
y=1(x+3)^2-1
or
y=(x+3)^2-1
Solve the Quadratic System
y=x-1
y=x^2+4x-5
(-4,-5)(1,0)
Graph the following quadratic function
f(x)=3(x+3)^2-29
vertex: (-3,-29) AOS x=-3 Yi (0,-2)
Write a Quadratic function in vertex form:
Vertex: (-3,5) Other point: (0,-14)
y=-19/9(x+3)^2+5
How do you find the vertex in standard form?
x value: -b/2a
plug than in for x and solve for y
Rewrite the quadratic function in vertex form f(x)=-x^2+4x-1
y=-(x-2)^2+3
Solve the Quadratic System
y=x^2-1
y=x-6
No Solution
Graph the quadratic function: f(x)=x^2+6x+5
Vertex: (-3,-4) Xi (-5,0) (-1,0) yi: (0,5)
Write a Quadratic function in factored form:
(-3,0) (0,-18)(1,-16)(3,0)
y=2(x+3)(x-3)
What is everything the a value tells you?
Up or down
Shrink or Stretch
Write the quadratic function in factored form
f(x)=x^2-16x+64
f(x)=(x-8)^2
or
f(x)= (x-8) (x-8)
Solve the Quadratic System
y=x^2-3x-4
y=-x-5
(1,-6)
Graph the following quadratic function
f(x)=-2 (x+3)(x-1)
xi: (-3,0)(1,0) aos x=-1 vertex (-1,8)
Write a Quadratic function in factored form:
(-4,0)(2,0)(-1,9)
Find the vertex:
f(x)=-x^2+6x-9
(3,0)
Rewrite the equation in factored form and find the zeros (XI)
f(x)=(x-1)^2-1
f(x)=x(x-2)
(0,0) and (2,0)
Solve the Quadratic System
y=2x^2-3x+5
y=2x+3
(2,7)(0.5,4)
Convert to factored form and then graph the quadratic
f(x)=x^2+2x-15
f(x)=(x+5)(x-3)
Vertex (-1,-16) Aos x=-1 xi (-5,0)(3,0) yi (0,-15)
Write the quadratic function in factored form
(-3,0) (-2,1.5) (-1,2) (0,1.5) (1,0) (2,2.5)
y=-1/2(x+3)(x-1)
Find the Vertex
g(x)=12(x+3)(x-1)
(-1,-48)
Rewrite the quadratic function f(x)=3x^2+12x+12 in vertex form and identify the vertex
Vertex: (-2,0)
f(x)=3(x+2)^2
Solve the Quadratic System
y=-x^2+2x-5
y=x^2-6x+3
(2,-5)