Question

What is the standard form of this function?
f(x) = (x-4)² + 2​

Answer 1

f(x)=x²-8x+18

Explanation:

f(x) = (x-4)² + 2​

To find the answer for the first part (x-4)², you need to use the formula.

This is the formula: (a-b)²=a²-2ab+b²

Plug in x for a and -4 for b.

(x-4)²=x²-8x+16

Now, put x²-8x+16 for (x-4)².

f(x)=x²-8x+16+2

Add like terms.

f(x)=x²-8x+18

Our answer is already in standard form because it is from greatest to least.

Hope this helps!

If not, I am sorry.

Answer 2

Standard form of quadratic equation: ax² + bx + c

Here given equation: f(x) = -(x - 4)² + 2

Simplify the equation:

⇒ f(x) = -(x - 4)² + 2

Use perfect square formula: (a + b)² = a² + 2ab + b²

⇒ f(x) = -(x² + 2(x)(-4) + (-4)²) + 2

⇒ f(x) = -(x² - 8x + 16) + 2

⇒ f(x) = -x² + 8x - 16 + 2

⇒ f(x) = -x² + 8x - 14

`\hrulefill`

Here given equation: f(x) = (x - 4)² + 2

Simplify the equation:

⇒ f(x) = (x - 4)² + 2​

⇒ f(x) = x² + 2(x)(-4) + (-4)² + 2

⇒ f(x) = x² - 8x + 16 + 2

⇒ f(x) = x² - 8x + 18