Question

The domain and range of 5x squared plus 10x what is the domain and range of f of x equals 5x squared plus 10x

Answer 1

Answer:

Domain:  set of all real numbers

Range:  $y \geq -5$

Step-by-step explanation:

We have to find the domain and range of the function:

$f(x) =5x^2+10x$

This is a quadratic function, shape of a "U", that's called a parabola.

The domain is the set of x values for which the function is defined.

The range is the set of y values for which the function is defined.

Normally, any parabola in the form  $ax^2+bx+c$  has domain as "all real numbers". This is the case for this problem as well, thus,

Domain = set of all real numbers

Now, for the range, we have to look at the minimum value of the function. So, the range would be y values greater than or equal to the minimum number. Lets find the minimum value of this function.

We have to find the value of x for which the minimum occurs by using the formula:

$x=\frac{-b}{2a} =\frac{-10}{2(5)} =-1$

Note: value of a is "5" and b is "10"

Now, we plug this into the function to find the minimum value:

$f(x)=5x^2+10x\\f(-1)=5(-1)^2 +10(-1)\\f(-1)=-5$

So, the range is set of all real numbers greater than or equal to -5.