Given the equation 5x2 − 20x + 15 = 0, what are the values of h and k when the equation is written in vertex form a(x − h)2 + k = 0? h = 2, k = 17 h = 2, k = −5 h = 1, k = 3 h = −1, k = −3
Accepted Solution
A:
Answer:h = 2, k = −5Step-by-step explanation:The given function is [tex]5x^2-20x+15=0[/tex]We need to complete the square to obtain the function in the form:[tex]a(x-h)^2+k=0[/tex]We factor 5 from the first two terms to get:[tex]5(x^2-4x)+15[/tex]We now add and subtract the square of half the coefficient of x.[tex]5(x^2-4x+4-4)+15[/tex][tex]5(x^2-4x+4)-5(4)+15[/tex][tex]5(x^2-4x+4)-20+15[/tex]Factor the perfect square expression within the parenthesis:[tex]5(x-2)^2-5[/tex]By comparing to [tex]a(x-h)^2+k=0[/tex], we have h=2 and k=-5