Question

Type the correct answer in the box. Rewrite the quadratic equation in the form y = a(x − h)2 + k. y=5x^2-30x+95

Answer 1

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