MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Warm Ups
Wednesday, March 23, 2016
Solve the equations.
1. x  7 x  4  10 2. x  22 x  121  0
2
2
x  11
x  6, x  1
3.
4 x  48
2
x  2 3
4.
x  13x  42
2
x  7, x  6
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Wednesday, March 23, 2016
Essential Question:
How do we find the zeros of a quadratic equation?
Lesson 3.4
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
3
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Solutions of a quadratic equation or function.
If y = f (x) is a quadratic function and a is a real number then the
following statements are equivalent.
1. x = a is a zero of f.
2. x = a is a root of f.
3. x = a is a solution of the quadratic equation f (x) = 0.
4. (x – a) is a factor of the quadratic f (x).
5. (a, 0) is an x-intercept of the graph of y = f (x).
4
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
1.
Find the zeros of the quadratic function.
Substitute zero for y.
2
Factor.
2
Apply the Zero Product Property.
y  x  3x  28
0  x  3x  28
 x  7x  4   0
x  7  0 or x  4  0
7  7
x  7
+4 +4
or
x4
The solutions are -7 and 4.
Solve both equations.
-28
+7
-4
+3
5
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Find the zeros of the function.
y  x  10 x  24
2
0  x  10 x  24
 x  6x  4   0
x  6  0 or x  4  0
2
2.
+4 +4
+6 +6
x6
or
x4
The zeros are 6 and 4.
Substitute y = 0.
Factor.
Apply the Zero Product Property.
Solve both equations.
+24
-6
-4
-10
6
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Find the zeros of the function.
Substitute y = 0.
Factor.
g ( x)  x  13x  12
2
0  x  13x  12 Apply the Zero Product Property.
x  12 x  1   0 Solve both equations.
x  12  0 or x  1  0
+12
2
3.
+1 +1
+12 +12
x  12
or
x 1
The zeros are 12 and 1.
-12 -1
-13
7
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Find the zeros of the function.
4.
g ( x)  x  11x
2
The zeros are 0 and 11.
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Find the zeros of the function.
5.
g ( x)  4 x  60 x
2
The zeros are 0 and -15.
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Find the zeros of the function.
6.
g ( x)   2 x  5  x  6 
2
The zeros are  , and 6
5
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Find the zeros of the function.
7. g ( x)   3 x  7  5 x  8 
The zeros are
7
8
, and
3
5
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Find the zeros of the function.
8. g ( x)   x  7  x  8 
The zeros are 7, and 8
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Find the zeros of the function, then write the equation.
9.
The zeros are  5, and 1
y   x  5 x  1
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Find the zeros of the function, then write the equation.
10.
The zeros are  2, and 6
y   x  2 x  6
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Find the zeros of the function, then write the equation.
11.
The zero is 3.
Double root!
y   x  3 x  3
y   x  3
2
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax2 +bx + c and f(x) = a(x – h)2 = k.
Guided Practice
Find the zeros of the function, then write the equation.
12.
The zeros are  4, and  1
y   x  4 x  1
MM2A4b Find real and complex solutions of equations by factoring, taking square roots, and applying the
quadratic formula.