To write the equation in graphing form, the x^2-term must have a coefficient of 1 so that we may complete the square.
B
b
To write the equation in graphing form, the x^2-term must have a coefficient of 1 so that we may complete the square.
A
a
Graphing Form: y=- 2(x-(- 14))^2+ 1058
Domain: All real numbers. Range: y≤ 1058 Is It a Function? Yes.
B
b
Graphing Form: y=- 3(x-(- 1))^2+15
Domain: All real numbers. Range: y≤ 15 Is It a Function? Yes.
Practice makes perfect
a
An equation in graphing form is written in the following format.
y=a(x-h)^2+k
To change the equation into this form, we have to complete the square. This requires that the coefficient of x^2 has to be 1. Therefore, before we can complete the square, we should first divide both sides of the equation by - 2.
y=-2x^2-x+13
⇓
y/- 2=x^2+1/2x-13/2
Now we can complete the square by adding the square of half the coefficient to x.
Having changed the equation to graphing form, let's draw its graph.
Is it a function?
Since there is no part of the graph where one x-value gives multiple y-values, we know that it is a function.
Domain and Range
There is no x-value that we cannot substitute into the equation, which means the domain must be all real numbers. The range shows the set of y-values or outputs a function can give. Since the function's maximum value is 1058, the range must be y≤ 1058.
Domain:& All real numbers [0.1em]
Range:& y≤ 105/8
b
Again, to write the equation in graphing form the coefficient of x^2 to be 1. Therefore, before we can complete the square, we should first divide both sides by - 3.
y=-3x^2-6x+12
⇓
y/- 3=x^2+2x-4
Now we can complete the square by adding the square of half the coefficient to x.
Having changed the equation to graphing form, let's draw its graph.
Is it a function?
Since there is no part of the graph where one x-value gives multiple y-values, we know that it is a function.
Domain and Range
There is no x-value that we cannot substitute into the equation, which means the domain must be all real numbers. The range shows the set of y-values or outputs a function gives. Since the function's maximum value is y=15, the range must be y≤ 15.
Domain:& All real numbers
Range:& y≤ 15
