Factoring Trinomials When a=1
Factoring Trinomials When a<1 or a>1
Key Attributes & Translate Between Forms
Formulas and Processes
About Quadratics
100
Factor the quadratic trinomial x^2-11x+24 into its binomial factors.
(x-3) and (x-8)
100
Factor the quadratic trinomial 2x^2+26x+80 into its binomial factors.
2(x+5)(x+8) or (2x+10)(x+8) or (x+5)(2x+16)
100
What are the 3 key attributes of a quadratic?
Vertex, y-intercept, and x-intercepts (roots, solutions, or zeroes)
100
What are the steps in converting vertex form to standard form?
1. Expand the binomial (or apply the exponent). 2. Distribute the a value. 3. Combine Like Terms.
100
What does it mean to solve a quadratic? In other words, what do the solutions represent on the graph?
To Solve a Quadratic is: to find the roots, zeroes, or x-intercepts (the places where the parabola crosses the x-axis)
200
Factor the quadratic trinomial x^2-5x-24 into its binomial factors.
(x+3) and (x-8)
200
Factor the quadratic trinomial 3x^2-39x+90 into its binomial factors.
3(x-3)(x-10) or (3x-9)(x-10) or (x-3)(3x-30)
200
Consider the quadratic function given by these three equations: f(x)=-3(x+4.5)^2+18.75 f(x)=-3x^2-27x-42 f(x)=-3(x+2)(x+7)
Vertex (-4.5,18.75) y-intercept (0,-42) Roots x={-2,-7}
200
What is the Quadratic Formula?
x=(-b[+or-](sqrt(b^2-4ac)))/2a
200
What special case quadratic only has one root?
A Perfect Square
300
Factor the quadratic trinomial x^2+26x+169 into its binomial factors.
(x+13)^2 or (x+13)(x+13)
300
Factor the quadratic trinomial 5x^2-25x-70 into its binomial factors.
5(x+2)(x-7) or (5x+10)(x-7) or (x+2)(5x-35)
300
What is they y-intercept of the function f(x)=2(x-0.5)^2-12.5?
(0,-12) Because f(x)=2x^2-2x-12
300
What is the standard form of a quadratic?
f(x)=ax^2+bx+c
300
When are the y-intercept and the vertex the same point?
When there is no linear term in the standard form of the vertex.
400
Factor the quadratic trinomial x^2-10x+25 into its binomial factors.
(x-5)^2 or (x-5)(x-5)
400
Factor the quadratic trinomial (1/3)x^2-5x+18 into its binomial factors.
(1/3)(x-6)(x-9) or ((1/3)x-2)(x-9) or (x-6)((1/3)x-3)
400
What are the roots of the function f(x)=2x^2-2x-12
x={3,-2} because f(x)=2(x-3)(x+2)
400
What is the intercept form of a quadratic?
f(x)=a(x-p)(x-q)
400
What special case quadratic has 2 roots, each the opposite of the other?
Difference of Squares
500
Factor the quadratic trinomial x^2-225 into its binomial factors.
(x-15) and (x+15) or (x+15)(x-15)
500
Factor the quadratic trinomial 0.5x^2+7x+24 into its binomial factors.
0.5(x+6)(x+8) or (0.5x+3)(x+8) or (x+6)(0.5x+4)
500
What are the roots (based on the intercept form) of the function f(x)=-0.5(x+12)^2+32
x={-4,-20} because f(x)=-0.5x^2-12x-40 and from there f(x)=-0.5(x+4)(x+20)
500
What is the vertex form of a quadratic?
f(x)=a(x-h)^2+k
500
What are the 3 methods for solving quadratic equations (that we have studied so far)?
1. Factoring 2. Taking Square Roots (Algebraically) 3. Quadratic Formula
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