Vertex to Standard and Standard to Vertex
Rewrite the function
f(x) = (x + 3)^2 + 2
in standard form.
x^2+6x+11
Which form of a quadratic function helps identify the vertex?
Which form helps identify the y-intercept?
Which form helps identify the x-intercepts?
Vertex form
Standard form
Factored form
Factor
x^2+3x-40
(x + 8)(x - 5)
3x^2-2x-5
(3x - 5)(x + 1)
Factor the GCF:
21a^2+3a
3a(7a+1)
Convert the standard form
f(x) = x^2 - 6x - 7
to vertex form.
f(x) = (x-3)^2-16
What is the vertex of the function
f(x) = 3(x - 1)^2 + 2?
(1, 2)
Factor
x^2-13x+42
(x - 6)(x - 7)
2x^2+11x+5
(2x + 1)(x + 5)
Factor by DOPS:
16x^2-49x^8
(4x+7x^4)(4x-7x^4)
Write the vertex form
f(x) = 3(x + 2)^2 - 5
in standard form
f(x) = 3x^2+12x+7
Does the function
f(x) = -2(x - 5)^2 + 3
open up or down?
Down
Factor
x^2-6x-27
(x - 9)(x + 3)
4x^2-15x-25
(x - 5)(4x + 5)
Factor by grouping:
3x³ - 6x² + 4x - 8
(3x^2+4)(x-2)
Convert the standard form
f(x) = x^2 + 4x + 3
to vertex form.
f(x) = (x+2)^2-1
What is the y-intercept of the following function
f(x) = x^2 - 4x - 5
(0, -5)
Factor:
x^2-19x+60
(x - 15)(x - 4)
2x^2+3x-9
(2x - 3)(x + 3)
Factor GCF:
4a³ - 3a²
a^2(4a-3)
Write the vertex form
f(x) = 2(x + 6)^2 - 8
in standard form
f(x) = 2x^2+24x+64
What are the x-intercepts of the following:
f(x) = (x -2)(x+5)
(2, 0) and (-5, 0)
Factor:
x^2-16x-80
(x - 20)(x + 4)
6x^2+5x-6
(2x + 3)(3x - 2)
factor by grouping:
3x³ + 4x² + 6x + 8
(x^2+2)(3x+4)