Rewrite the quadratic function in standard form.
f(x)= x^2 - 8x + 36
I got f(x)= (x-4)^2 + 20
Am I right or wrong?
that is the vertex form, not the standard form.
You want
(x-h)^2 = a(y-k)
Most authors of Calculus texts classify them as:
1) Standard form: y = ax^2 + bx + c where the a,b, and c are just real numbers.
2) Factored form: y = (ax + c)(bx + d) again the a,b,c, and d are just numbers.
3) Vertex form: y = a(x - b)^2 + c again the a, b, and c are just numbers and (b,c) is the vertex.
Isn't that in Standard form already then?
f(x) = x^2 - 8x + 36
y = ax^2 + bx +c
Or am I missing something?
Take a look how the author of your text or your teacher defines "standard form"
then state the matching equation.
To rewrite the quadratic function in standard form, you need to expand and simplify the expression.
Given the quadratic function:
f(x) = x^2 - 8x + 36
To rewrite it in standard form, you need to remove any parentheses and combine like terms. Let's go through the steps:
1. Start with the given expression:
f(x) = x^2 - 8x + 36
2. Expand the squared term:
f(x) = (x - 4)(x - 4) + 36
Using the FOIL method to multiply the binomials:
f(x) = x^2 - 4x - 4x + 16 + 36
3. Combine like terms:
f(x) = x^2 - 8x + 52
Therefore, the correct standard form of the quadratic function is:
f(x) = x^2 - 8x + 52
So, your answer f(x) = (x - 4)^2 + 20 is incorrect. The correct standard form is f(x) = x^2 - 8x + 52.