Question

the vertex form of the equation of a parabola is y=(x-5)2+16. what is the standard form of the equation

Answer 1

y = x² - 10x + 41

Explanation:

The standard form of a quadratic is ax² + bx + c : a ≠ 0

Given

y = (x - 5)² + 16 ← expand (x - 5)²

= x² - 10x + 25 + 16

= x² - 10x + 41 ← in standard form

Answer 2

Answer:
`y=x^2-10x+41`

Explanation:

The standard form of a quadratic function is:

`y=ax^2+bx+c`

You need to remember the square of a binomial:

`(a-b)^2=a^2-2ab+b^2`

Applying the above, you get:

`y=(x-5)^2+16`

`y=(x^2-2(x)(5)+5^2)+16`

Simplify the expression:

`y=x^2-10x+25+16`

Now you need to add the like terms.

THerefore, you get:

`y=x^2-10x+41`