What is the vertex form of the parabola whose standard form equation is y=5x^2-30x+49

The vertex is (3,4)

Step-by-step explanation:

To convert a quadratic from

y = a x 2 + b x + c

form to vertex form,

y = a (x - h) 2 + k, you use the process of completing the square.

First, we must isolate the x

terms:

y - 49 = 5 x 2 - 30 x + 49 - 49

y - 49 = 5 x 2 - 30 x

We need a leading coefficient of 1

for completing the square, so factor out the current leading coefficient of 2.

y - 49 = 5 (x 2 - 6 x)

Next, we need to add the correct number to both sides of the equation to create a perfect square. However, because the number will be placed inside the parenthesis on the right side we must factor it by

2

on the left side of the equation. This is the coefficient we factored out in the previous step.

y - 49 + (5 ⋅?) = 5 (x 2 - 6 x + ?)

< - Hint:

62 = 3; 3 ⋅ 3 = 9

y - 49 + (5 ⋅ 9) = 5 (x 2 - 6 x + 9)

y - 49 + 45 = 5 (x 2 - 6 x + 9)

y - 4 = 5 (x 2 - 6 x + 9)

Then, we need to create the square on the right hand side of the equation:

y - 4 = 5 (x - 3) 2

Now, isolate the y term:

y - 4 + 4 = 5 (x - 3) 2 + 4

y - 0 = 5 (x - 3) 2 + 4

y - 0 = 5 (x - 3) 2 + 4

The vertex is:

(3, 4)