Question

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

Answer 1

Answer:

h = 2, k = −5

Step-by-step explanation:

The given function is $5x^2-20x+15=0$

We need to complete the square to obtain the function in the form:

$a(x-h)^2+k=0$

We factor 5 from the first two terms to get:

$5(x^2-4x)+15$

We now add and subtract the square of half the coefficient of x.

$5(x^2-4x+4-4)+15$

$5(x^2-4x+4)-5(4)+15$

$5(x^2-4x+4)-20+15$

Factor the perfect square expression within the parenthesis:

$5(x-2)^2-5$

By comparing to $a(x-h)^2+k=0$, we have h=2 and k=-5

Answer 2

Answer:

h=2, k=-5

Step-by-step explanation: