Formulas and Stuff
Standard Form of a Quadratic Equation?
y = ax2+bx+c
When factoring, what is the first thing you should try to factor out?
Greatest Common Factor (GCF)
What is a vertex?
a point that is either at the very top or bottom of a parabola
What are the a and b values for the following equation?
-2x2+5x-3
a = -2 and b = 5
Which is the x-axis? Horizontal or vertical?
Horizontal
Factored Form of a Quadratic Expression?
(x+#)(x+#)
Fill in the blanks:
When factoring, you need to find something that ____ to the c value, but ____ to the b value.
When factoring, you need to find something that multiplies to the c value, but adds to the b value.
Once you have found the h-value, how do you find the k-value?
What are the a and b values of the following equation:
x2-9x
a = 1 and b = -9
When a is positive, is the graph facing up (smiling) or facing down (frowning)?
up
Vertex Form of a Quadratic Equation?
y = a(x-h)2+k
The factored form of 9x2 - 16
(3x-4)(3x+4)
Given the vertex of (3, -2) and an a-value of 1, write an equation in vertex form.
(x-3)2-2
Put the following factored quadratic into standard form: (x+7)(x-2)
x2+5x-14
When a is negative, is the graph facing up (smiling) or facing down (frowning)?
Coordinates of the Vertex (in letters)
(h, k)
x-intercepts
Given the vertex of (-2, 3) and an a-value of -4, write an equation in vertex form.
-4(x+2)2+3
Put the following factored quadratic into standard form: (x-3)2
x2-6x+9
What three points do you use to graph a parabola?
The x-intercepts (zeros) and the vertex
Formula used to find the x-value of the vertex?
x = -b/2a
Factor the following equation:
x2-x-6
(x-3)(x+2)
Given this equation, in standard form, rewrite it into vertex form.
x2 – 2x – 8
(x – 1)2 – 9
Put the following vertex form quadratic into standard form: -2(x-3)2+5
-2x2+12x-13
Given the zeros of x = 5 and x = -5 and a vertex of (0,8), is the parabola facing up (smiling) or down (frowning)?
Down