If a, h and k are positive constants, how many times will the graph of y = a(x – h)2 + k intersect the x-axis?

Question

Help I don't really get the question.

Answer 1

Hi Adriana,

y = a(x-h)² + k will intercept the x-axis at y = 0

a(x-h)² + k =0

ax² - 2ahx + ah²+k = 0 use the quadratic formula

 

a= a, b = -2ah, c = ah²+ k

x= (-b ±√(b² - 4ac) )/2a

  = (2ah ±√(4(ah)² -4a(ah² + k))/2a

  = (2ah ±√(4(ah)² -4(ah)² -4ak))/2a

  = (2ah ± 2√-ak)/2a

  = h ± (1/a)√-k

since k > 0, √-k is an imaginary number, there are no  x-axis intercepts

if k <0 there are two intercepts

The intercepts  are ( h +(1/a)√-k, 0) and (h -(1/a)√-k, 0)