Mathematics 10 Page 1 of 7 Verte form of Quadratic Relations The epression a p q defines a quadratic relation called the verte form with a horizontal translation of p units and vertical translation of q units. The verte of the quadratic relation is p, q and ais of smmetr is at a. A quadratic relation in verte form a p q epanding and collecting like terms. can be converted to standard form a b c b a p q a p p 0 & q 0 Verte : a 0 p, q Ais of Smmetr : p Reflects about - ais Concaves down p, q p, q p 0 & q 0 Verte : p, q a 0 Concave up q Ais of Smmetr : p intercepts p q a intercept ap q Basic Points of a Quadratic Relation (Parabol -3 - -1 0 1 3 Step Patterns: Eample 1: Parabola with a Vertical Translation Given the quadratic relation, determine the intercepts, intercept, direction of opening, ais of smmetr and the verte. Determine a mapping rule and a sketch of the relation on the given grid. Describe the translation. 4, -3 - -1 0 1 3
Mathematics 10 Page of 7 Eample : Parabola with a Horizontal Translation Given the quadratic relation, determine the intercepts, intercept, direction of opening, ais of smmetr and the verte. Determine a mapping rule and a sketch of the relation on the given grid. Describe the translation. 3, -3 - -1 0 1 3,,
Mathematics 10 Page 3 of 7 Eample 3: Parabola with Translations Given the quadratic relation, determine a mapping rule and a sketch of the relation on the given grid. Describe the translation. 3, Eercise 1. Complete the chart: 4 7 e) 5 f) 1 verte -intercepts (if an) -intercept direction that curve opens equation of ais of smmetr. Graph the following equations on the same set of aes using the answers ou found in question 1. Label each parabola with its corresponding equation. e) f) 4 7 5 1
Mathematics 10 Page 4 of 7 3. Describe the effect of various values of "q" on the graph of q 4. Which graph best represents each of the following. (Label the graph with the appropriate letter) 3 3 1 5. Write an equation that could correspond to each graph: a b c d 6. Fill in the following chart: 5 direction of opening coordinates of verte -intercepts (if an) -intercept 3 4 7. For the general quadratic q : What are the co-ordinates of the verte? What restriction on the value of q eists in order for -intercepts to eist?
Mathematics 10 Page 5 of 7 8. Complete the chart for each equation. e) f) g) ( ) ( 4) ( 3) ( 6) ( 4) ( 6) verte equation of ais of smmetr -intercepts (if an) -intercept 9. Graph the following equations on the same set of aes using the answers ou found in question 8. Label each parabola with its corresponding equation. ( 3) f) ( 4) ( ) e) ( 6) g) ( 6) ( 4) 10. Compare the graphs of and ( p) when: p > 0 p < 0
Mathematics 10 Page 6 of 7 11. Which graph best represents each of the following. Label with appropriate letter. ( 1) ( ) ( 4) ( 4) 1. Write an equation that could correspond to each graph: d c b a 13. Complete the following chart: co-ordinates of verte equation of ais of smmetr direction of opening -intercept (if an) -intercept ( 3) ( 8) ( ) e) ( 4)
Mathematics 10 Page 7 of 7 Answers 1 Verte: (0,0), -int: 0, -int: 0, opens up, = 0 Verte: (0,4), -int: NA, -int: 4, opens up, = 0 Verte: (0,7), -int: NA, -int: 7, opens up, = 0 Verte: (0,-), -int:, -int: -, opens up, = 0 e) Verte: (0,-5), -int: 5 -int: -5, opens up, = 0 f) Verte: (0,1), -int: NA, -int: 1, opens up, = 0 3) Vertical translations b q units a, d, c, b 4) 5) 5 3 4 1 6 Opens up, Verte: (0,5), -int: NA, -int: 5 7 (0, q) q < 0 Opens up, Verte: (0,-3), -int: 3, -int: -3 Opens up, Verte: (0,), -int:na, -int: Opens up, Verte: (0,4), -int:na, -int: 4 8 Verte: (0,0), = 0, -int: 0, -int: 0 10. p > 0 Right b p. Verte: (,0), =, -int:, -int: 4 p < 0 Left b p Verte: (-4,0), = -4, -int: -4, -int: 16 Verte: (-3,0), = -3, -int: -3, -int: 9 e) Verte: (6,0), = 6, -int: 6, -int: 36 f) Verte: (4,0), = 4, -int: 4, -int: 16 g) Verte: (-6,0), = -6, -int: -6, -int: 36 11. 1) ( 5) ( 1) ( 3) ( 6) c b a d 13 Verte: (0,0), = 0, opens up, -int: 0, -int: 0 Verte: (-3,0), = -3, opens up, -int: -3, -int: 9 Verte: (8,0), = 8, opens down, -int: 8, -int: -64 Verte: (,0), =, opens up, -int:, -int: 4 e) Verte: (-4,0), = -4, opens down, -int: -4, -int: -16