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

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

Step-by-step 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:

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

Answer 2

Answer:

y = x² - 10x + 41

Step-by-step 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