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標題:

Quadratic 呀~~help me!!!

發問:

5. The y-intercept of the graph of the quadratic equation in two unknowns y=a(x-h)^2 -25/2 is 12. One of the x-intercepts of the graph of the equation is 6.(我想要步驟~唔該)(a) Find the values of a and h (Ans: a=2, h=7/2, a=1/18, h=21)(b) Find the other x-intercept of the... 顯示更多 5. The y-intercept of the graph of the quadratic equation in two unknowns y=a(x-h)^2 -25/2 is 12. One of the x-intercepts of the graph of the equation is 6.(我想要步驟~唔該) (a) Find the values of a and h (Ans: a=2, h=7/2, a=1/18, h=21) (b) Find the other x-intercept of the graph.(Ans: 1 ; 36)

最佳解答:

a) Since one of the x-intercept is 6 and the y-intercept is 12 by putting (6,0) and (0,12) into y=a(x-h)^2-(25/2) we have: a(6-h)^2=25/2---(1) ah^2=49/2---(2) (1)/(2): [(6-h)/h]^2=25/49 (6-h)/h=5/7 or (6-h)/h=-5/7 h=7/2 or h=21 by putting h=7/2 and h=21 into (2) on solving , the solutions are (a=2, h=7/2) or (a=1/18, h=21) b) for a=2, h=7/2 y=2(x-(7/2))^2-(25/2) set y=0, (x-(7/2))^2=25/4 x-(7/2)=5/2 or x-(7/2)=-5/2 x=6 (rejected) or x=1 for a=1/18, h=21 y=(1/18)(x-21)^2-(25/2) set y=0, (x-21)^2=225 x-21=15 or x-21=-15 x=36 or x=6 (rejected) Hence , the other x-intercepts of the graph are 1 and 36.

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