Question

What is the standard form of the equation of f(x)?

Answer 1

The standard form of an equation depends on the type of function f(x) you are referring to. Here are some examples of standard forms for commonly used functions:

Linear function: f(x) = mx + b, where m is the slope of the line and b is the y-intercept.

Quadratic function: f(x) = ax^2 + bx + c, where a, b, and c are constants. This is also called the "vertex form" of the quadratic function.

Exponential function: f(x) = ab^x, where a and b are constants. This is also called the "base exponential form" of the function.

Logarithmic function: f(x) = loga(x), where a is the base of the logarithm.

There are many other types of functions, and each one has its own standard form.

Explanation:

Answer 2

The standard form of the parabolic equation is determined as y = - (x - 2)² + 16.

How to write the standard equation of the function?

The standard form of the equation for a parabolic curve is given by:

y = a (x - h)² + k

where;

• (h, k) is the vertex of the parabola

From the curve we can see that x - coordinate of the vertex, h = 2,

and the y - coordinate of the vertex, k = 16

The value of a is calculated as follows;

y = a (x - h)² + k

y = a (x - 2)² + 16

Using the roots of the equation; x = - 2 or x = 6

at x = -2, y = 0

0 = a (-2 - 2)² + 16

0 = 16a + 16

16a = - 16

a = - 1

The standard form of the parabolic equation becomes;

y = - (x - 2)² + 16