4.6 Q UADRATIC EQUATION AND THE D ISCRIMINANT. Q UIZ : S OLVE BY USING THE QUADRATIC FORMULA.

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Presentation transcript:

4.6 Q UADRATIC EQUATION AND THE D ISCRIMINANT

Q UIZ : S OLVE BY USING THE QUADRATIC FORMULA

C AN YOU SIMPLIFY THE FORMULA ?

W HAT IF IT IS NOT IN STANDARD FORM ? 2x = 3x² + 5 (Hint: Remember what you do to the left you do to the right) 0 = 3x² + 2x + 5 a = ?, b = ?, c = ? a = 3, b = 2,c = 5

Y OUR T URN : Y = ax² + bx + c 0 = ax² + bx + c Define the values : a = ?, b = ?, c = ? 1. Y = 2 – 12x² x = 3x² - 5x Y = 3x + 4x² + 7

T HE EQUATIONS CAN RESULT IN MORE COMPLICATED ARITHMETIC

Y OUR T URN :

Y OUR T URN : U SE THE Q UADRATIC E QUATION TO SOLVE 5. y = x² , y = x² - 2x Which one of the equations is in standard form? a) y = 2 (x – 4)² + 13 b) y = 5 ( x – 3)( x – 4) c) y = 5x² + 6x + 8

U SE THE QUADRATIC E QUATION TO SOLVE 8. y = x² - 4x + 4 (Solve using the quadratic equation) 9.Why does the equation only have 1 x-intercept? 10. What happened to the quadratic equation to have the equation produce 1 x – intercept?

Y OUR T URN : U SE THE QUADRATIC TO SOLVE 11. y = x² + 4x + 4 (Use the quadratic equation). 12. What are the x-intercepts of the parabola? Does it cross the x axis 13. What happened in the quadratic equation that made the x-intercepts different? What kind of x- intercepts are they?

14. W HICH ONE OF THE FOLLOWING EQUATIONS WILL HAVE IMAGINARY SOLUTIONS ?

15. W HICH ONE OF THE FOLLOWING EQUATIONS HAS ONLY ONE X - INTERCEPT ?

V OCABULARY : D ISCRIMINATE

Y OUR T URN : 16. Write the part of the quadratic that is the discriminate.

W HAT HAPPENS IF THE DISCRIMINATE IS A POSITIVE NUMBER ?

W HAT H APPENS WHEN THE D ISCRIMINATE IS ZERO ?

H OW DOES IT ONLY TOUCH THE X - AXIS IN ONLY ONE PLACE y = x² + 4x + 4 (perfect square trinomial) Y = ( x + 2 ) ² Y = ( x + 2 ) ( x + 2 ) 0 = ( x + 2) ( x + 2) X = -2 What does the graph look like?

W HAT HAPPENS IF THE DISCRIMINATE IS NEGATIVE ?

T HE DISCRIMINATE IN THE RADICAND OF THE QUADRATIC EQUATION :

Y OUR TURN : Find the discriminate of the following equations: 17. y = x² - 2x y = x² - 2x – y = x² - 4x How many solutions for problem #17? 21. How many solutions for problem # 18? 22. How many solution for problem # 19?