How many solutions does your quadratic have?

4 3 2 1 0In addition to level 3, students make connections to other content areas and/or contextual situations outside of math.

 

Students will sketch graphs of quadratics using key features and solve quadratics using the quadratic formula. - Students will be able to write, interpret and graph quadratics in vertex form.

Students will be able to use the quadratic formula to solve quadratics and are able to identify some key features of a graph of a quadratic.

Students will have partial success at a 2 or 3, with help.

Even with help, the student is not successful at the learning goal.

Focus 10 Learning Goal – (HS.A-REI.B.4, HS.F-IF.B.4, HS.F-IF.C.7, HS.F-IF.C.8) = Students will sketch graphs of quadratics using key features and solve quadratics using the quadratic formula.

Solve the following three quadratics using only the quadratic formula. Show your work. 1. x2 – 2x + 1 = 0

2. 3x2 + 4x + 8 = 0

3. 2x2 + 7x - 4 = 0

Describe these three solutions.

What do you notice about the formula while you were solving it that provided you with these answers?

The expression under the radical is called the discriminant: b2 – 4ac

The value of the discriminant determines how many solutions the quadratic will have.

Equation 1: the discriminant was zero, there was only 1 solution.

Equation 2: the discriminant was a negative number, there was no solution.

Equation 3: the discriminant was a positive number, there were two solutions.

Remember: when we solve a quadratic, we are finding where the parabola intercepts the x-axis.

What is the difference between these three graphs? Which of these three graphs belongs to a quadratic with a

positive discriminant? Which belongs to a quadratic with a negative

discriminant? Which graph has a discriminant equal to zero?

Without solving, determine the number of real solutions for each quadratic equation.

1. x2 + 7x + 33 = 8 – 3x

1. x2 + 10x + 25 = 0

2. (102) – 4(1)(25)

3. 0

4. One real solution

2. 7x2 + 2x + 5 = 0

1. (22) – 4(7)(5)

2. 4 – 140

3. -136

4. No real solutions

3. 2x2 + 10x = x2 + 4x - 3

1. x2 + 6x + 3 = 0

2. (62) – 4(1)(3)

3. 24

4. Two real solutions

4. 4x2 + 9 = -4x

1. 4x2 + 4x + 9 = 0

2. (42) – 4(4)(9)

3. 16 – 144

4. -128

5. No real solutions

State whether the discriminant of each quadratic is positive, negative, or equal to zero. Then identify which graph matches the discriminants below.

Graph #2 Graph #1 Graph #4 Graph #3