5.3 Discriminant and 5.4Find ABC

Discriminant: b2 – 4ac

A, B, C ax2 + bx + c = 0

5.3 Discriminant and 5.4 Find ABC

Always remember that MT5 revolves around the topic of this shape

The graph of a Quadratic is called a Parabola

Sometimes the shape can move around…

5.3 Discriminant and 5.4 Find ABC

The points where the line crosses the X Axis are called roots (zeros)

Roots

5.3 Discriminant and 5.4 Find ABC

How many roots for each shape?

A)

B)

C) A

B

C

0

1

2

Awesome Job!

5.3 Discriminant and 5.4 Find ABC

The Discriminant is a shortcut for finding out how many possible roots a parabola (graph of a quadratic) has without having to graph it. The formula is this…

b2 – 4ac

We get our input from this equation…

ax2 + bx + c = 0

5.3 Discriminant and 5.4 Find ABC

Here’s what a problem will look like

How many possible roots in this equation: 3x2 + 4x - 5

42 – 4(3)(-5)

Here’s how to solve:

3x2 + 4x - 5a b c

A = 3B = 4 C = -5

Now Plug It In!

b2 – 4ac

5.3 Discriminant and 5.4 Find ABC

Here’s what a problem will look like

How many possible roots in this equation: 3x2 + 4x - 5

42 – 4(3)(-5)Now solve:

That’s it!

16 - – 60

16 + 60

76

5.3 Discriminant and 5.4 Find ABC

Here’s what a problem will look like

How many possible roots in this equation: 3x2 + 4x - 5

Finally: You must remember this part…

Positive Answer: 2 RootsZero (0): 1 RootNegative Answer: No Roots

Your homework requires you to have three answers. In this problem your answer would be…A = 3B = 4 76 and 2 rootsC = -5

5.3 Discriminant and 5.4 Find ABC

Let’s practice the possible roots part…

Please figure out how many possible roots

1. 25

2. - 18

3. 0

4. -6

2 roots (positive)

No roots (negative)

1 root (zero)

No roots (negative)