作者:Patel Sheil 7 年以前
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X-coordinate of the vertex of a parabola is -b/2a and the equation of the axis of symmetry is x=-b/2a
Substitute into the y= a(x-r)(x-s) formula
To find an equation that represents the relation
Write equation in standard form and then factor the left side
Set each factor equal to zero and solve for the unknown
Allows you to find the min or max point of a quadratic relation of the form y= ax^2 + bx + c algebraically
When you multiply the sum and the difference of two terms, the two middle terms are opposites so they add to zero, so you just multiply the rest.
When squaring a binomial, you add the two equal middle terms after expansion and square the rest.
Perfect Square Trinomial
Factor using this formula: a^2 + 2ab + b^2
Difference of Squares
Factor using this formula: a^2 - b^2 = (a + b) (a - b)
Quadratic expression
ax^2 + bx + c
Find two integers whose product is a * c and whose sum is b. Then break up the middle term and factor by grouping
x^2 + bx + c
First find two integers, whose product of c is the sum to b
Grouping
Factor groups of two terms with a common factor to produce a binomial common factor.
Find the GCF of the Polynomial
First find the GCF of the coefficients and then the GCF of the variable parts
Remove the GCF as the first factor, and then divide each term by the GCF to find the second factor
Use the Distributive Property
Downward
"a" value is negative
Maximum value
Upward
"a" value is positive
Minimum value
Y-Intercept
Make the x-value as 0
X-Intercept
There are 2 x-intercepts
Can be either positive or negative
Make the y-value as 0
"a" value stretch or compress the graph vertically by a factor of a
a>1 or a<-1 = graph is stretched vertically (narrows)
a<0 = reflected in the x-axis
"h" value translated the graph horizontally
h<0 = translated to the left
h>0 = translated to the right
"k" value translates the graph vertically
k<0 = translated downward
k>0 = translated upward
Any set of real numbers
If a < 0 then y is less than or equal to k
If a > 0 then y is greater than or equal to k
1a, 3a, 5a
Seperate radicals
Negative reciprocal
Multiply exponents
Subtract exponents
Add exponents
Using a table of values chart
Second differences are constant
The (x,y) coordinates of the vertex are the (h,k) values in the vertex equation
Goes through the vertex
Curve of best fit
Smooth curve drawn to approximate the general path or trend in a scatter plot