Answer:
y = 5(x - 3)^2 + 50
Step-by-step explanation:
The problem wants you to rewrite the quadratic equation in the vertex form y = a(x - h)^2 + k
You are given a quadratic equation in standard form (ax^2 + bx = c).
To convert from standard form to vertex form, there are two ways but I will show you the easier(?) way.
Use the formula x = -b/2a to find the x-value (h) of the vertex. Note that the vertex in "vertex form" is (h, k) which is virtually the same as (x, y).
In y = 5x^2 - 30x + 95, a = 5, b = -30, and c = 95. Substitute a and b into the formula -b/2a.
-(-30) / 2(5)
Two negative make a positive, so -(-30) becomes 30 and 2 times 5 is 10. Now we have:
30/10 which simplifies down to 3.
The x (h) value of the vertex is 3. To find the y-value, substitute 3 into the original standard form equation.
y = 5(3)^2 - 30(3) + 95
= 5(9) - (90) + 95
45 - 90 + 95
50
The y (k) value of the vertex is 50. Now we have: (h, k) ⇒ (3, 50).
Substitute the values for h and k into the vertex form.
y = a(x - 3)^2 + 50
We still need the a-value, and this is easy to find. You take the a value from the original standard for equation (remember: ax^2 + bx + c)
So our a-value is 5. Now we can substitute this value into the vertex form and complete the question.
y = 5(x - 3)^2 + 50
