Put the equation y=x^2-10x+24 into the form y=(x-h)^2+k
x^2-10x+24
= x^2 - 10x + 25 - 1
= (x-5)^2 - 1
To rewrite the equation y = x^2 - 10x + 24 in the form y = (x - h)^2 + k, we need to complete the square.
1. Start by taking out the common factor from the first two terms: y = (x^2 - 10x) + 24.
2. Next, take half of the coefficient of x (-10) and square it: (-10/2)^2 = (-5)^2 = 25.
3. Add this value inside the parentheses and subtract it outside the parentheses: y = (x^2 - 10x + 25 - 25) + 24.
This step helps us create a perfect square trinomial.
4. Simplify the equation: y = (x^2 - 10x + 25) - 25 + 24.
5. Combine the constants: y = (x^2 - 10x + 25) - 1.
6. Rewrite the squared trinomial as a perfect square: y = (x - 5)^2 - 1.
Now the equation is in the form y = (x - h)^2 + k, where h is 5 and k is -1.
To put the equation y=x^2-10x+24 into the form y=(x-h)^2+k, we need to complete the square.
Step 1: Group the terms involving x^2 and x together:
y = (x^2 - 10x) + 24
Step 2: Take half of the coefficient of x (-10/2 = -5) and square it (-5)^2 = 25. Add and subtract this value inside the parentheses to maintain the equation's balance:
y = (x^2 - 10x + 25 - 25) + 24
Step 3: Rearrange the terms:
y = (x^2 - 10x + 25) - 25 + 24
Step 4: Rewrite the trinomial as a perfect square:
y = (x - 5)^2 - 1
Now the equation is in the form y = (x - h)^2 + k, with h = 5 and k = -1.