Quadratics, Right Triangle Trigonometry, Circles And Spheres, Statistics, Algebraic Models For Quantitative Data Worksheet Page 3
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12STANDARD: SOLVE QUADRATICS
21. Solve the equation
by using the
quadratic formula.
Graphically - Simply look to see where the graph intersects
the x-axis.
Factoring - Use the “Big X”. Must be in standard form first!
Find 2 numbers that multiply to be c and add to be b. These
are called the factors. Set each factor equal to 0 and solve for
x to find the solutions.
Quadratic Formula - Identify the a, b, and c values. Must be
in standard form first! Plug the a, b, and c values into the
22. Sketch the function
.
quadratic formula.
10
o
Simplify to solve for x.
√
8
o
6
4
Discriminant - The discriminant is the number under the
2
radical of the quadratic formula,
. Must be in
standard form first!
-10 -8 -6 -4 -2
2
4
6
8 10
o
If the discriminant is positive, there are 2 real
-2
solutions.
-4
o
If the discriminant is 0, there is 1 real solution.
-6
o
If the discriminant is negative, there are 2 imaginary
-8
solutions.
-10
Quadratic Inequalities - Look at the inequality sign to
23. Determine whether the following points are a
determine if you need a solid or dotted line. If the inequality
solution to the inequality
.
is
or , use a dotted line. If the inequality is
or , use a
solid line.Test a point either inside or outside of the parabola
a.
to see if it is a solution. Shade the area of the graph that is
the solution to the inequality.
b.
18. Determine the types of roots for the graphed
quadratics.
c.
24. Determine the solutions to the graphs.
19. Find the value of the discriminant and explain the
types of solutions for the quadratic
.
25. Find the solutions to the equation
20. Find the solutions of the equation
.
.
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