1. Grade 10 Academic (MPM2D) Unit 4: Quadratic Relations Discriminants of Quadratics
Mr. Choi
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2. Summary: Quadratic Formulas Vertex Form:
Axis of Symmetry:
x-intercepts:
y-intercept:
Standard Form:
Vertex:
Axis of Symmetry:
x-intercepts:
y-intercept:
Discriminants of Quadratics
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3. Quadratic formula is used to find the roots of the quadratic relation
Recall:
Quadratic formula is used to find the roots of the quadratic relation
To find the roots:
let and , then
Note that in the quadratic formula, the value of
determines the number and type of roots a quadratic equation has.
This expression is called the discriminant.
2 real roots
1 real root
no real roots
When using the quadratic formula,
If then the quadratic equation has 2 real roots.
If then the quadratic equation has 2 equal real roots (1 real root).
If then the quadratic equation has No real roots.
Discriminants of Quadratics
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4. Example 1: Discriminants Determine how many roots each equation has
Discriminants of Quadratics
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5. Example 1: Discriminants Determine how many roots each equation has
Different thinking!!
(7, -12)
Different thinking 2!!
Vertex: (7, -12)
Vertex form:
Since the vertex is (7, -12) and the parabola is opens up, therefore there are two zeros. The equation has two roots.
Discriminants of Quadratics
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6. Example 2: Discriminant
For , determine how many x-intercepts each relation has.
Determine the key features (intercepts, axis of symmetry, vertex) of the parabola. Sketch the parabola.
Method 1:
Method 2:
2 equal real roots
Or 1 real root at
x = 2.
x- intercepts:
y - intercept:
Axis of symmetry:
Vertex:
Discriminants of Quadratics
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7. Homework
Work sheet: Discriminants of Quadratics: Functions and Relations Text: P. 403 #5 Check the website for updates
Discriminants of Quadratics
© 2017 E. Choi – MPM2D - All Rights Reserved

8. End of lesson Discriminants of Quadratics
© 2017 E. Choi – MPM2D - All Rights Reserved