Identify Key Features
What key features can you identify from the equation?y=-1/2(x-4)^2+2
Vertex (4,2)
Opens down
Vertical compression by a factor of 1/2
Write the quadratic equation for the parabola has a vertex of (-9,8) with no vertical compression or stretch, and opens up.
y=(x+9)^2+8
Convert the equation into STANDARD form.
y=(x-5)^2+3
y=x^2-10x+28
factor using GCF
6x^3 + 7x^2
x(6x^2 + 7x)
factor
x^2-4
(x-2)(x+2)
factor
x^2 + 13x + 12
(x+12)(x+1)
What key features can you identify in the equation?
y=2(x+3)(x-4)
X-intercepts (-3,0) and (4,0)
Opens up
Vertical stretch by a factor of 2
Write a quadratic equation for the parabola with zeros at 5 and -8, with a vertical stretch of 3 and opens up.
y=3(x-5)(x+8)
Convert the vertex form equation into STANDARD form.
y=2(x+4)^2-5
y=2x^2+16x+27
Factor
25x^4+35x-15
5(5x^4+7x-3)
FACTOR
4x^2-9
(2x-3)(2x+3)
FACTOR
x^2 − 13x + 36
(x-9)(x-4)
What key features can you identify in the equation?
y=2/3(x+3)^2-1
Vertex of (-3,-1)
Opens up
Vertical compression
Write the equation of a parabola with a vertex of (-4,-2) that has a vertical compression of 1/3 and opens down.
y=-1/3(x+4)^2-2
Convert the equation in FACTORED form
x^2-12x-19=-3x+17
y=(x-12)(x+3)
(x-12)(x+3)=0
FACTOR
21x^6 -2x^4-5x^2
x^2(21x^4 -2x^2-5)
x^2-81
(x-9)(x+9)
FACTOR
2x2 + 14x - 16
2(x-1)(x+8)
What key features can you identify in the equation?
y=2x^2 + 14x - 16
y-intercept (0,-16)
Opens up
Vertical stretch
Write the equation of a parabola that has roots of -4 and 8, a vertical stretch of 2, and opens downwards.
y=-2(x+4)(x-8)
Convert the equation into factored form.
12x^2 - 20=8x
y=4(x-1)(3x+5)
4(x-1)(3x+5)=0
FACTOR
21x^6 + 7x^4+7x^3
7x^3(3x^3 + x+1)
FACTOR AND SOLVE
3x^2-27=0
3(x-3)(x+3)
x=-3
x=3
FACTOR AND SOLVE
3x^2 +10x +8=0
(3x+4)(x+2)
x=-2
x=-4/3
What key features can you identify in the equation?
y=-3(x+1/2)^2
Vertex (-1/2,0)
Opens down
Vertical stretch
Write the equation of parabola that has a vertex of (2,0), a vertical compression of 1/4, and was reflected across the x-axis.
y=-1/4(x-2)^2
Convert the vertex form equation into STANDARD form.
y=-4(x-7)^2-6
y=-4x^2+56x-202
FACTOR & SOLVE
36x^2+12x=-8x
4x(9x+5)=0
x=0
x=-5/9
FACTOR & SOLVE
16-81x^2=0
-1(9x+4)(9x-4)
x=-4/9
x=4/9
FACTOR AND SOLVE
5x^2 + 14x - 10=3x^2+6
2(x-1)(x+8)
x=1
x=-8