How do you find the intercepts, vertex and graph f(x)=x^2+12x+36?

1 Answer
Feb 7, 2017

x-intercept: (-6, 0)

y-intercept: (0, 36)

vertex: (-6, 0)

Explanation:

graph{x^2+12x+36 [-133.2, 26.8, -8.86, 71.14]}

To find the y-intercept, substitute 0 in for x, which will give you an answer of

f(x) = 36

To find the x-intercepts, (also known as zeros or roots), substitute 0 in for f(x) (which is the y value in this case).

Since this is a polynomial with a degree of 2 (which just means that the highest exponent is 2), you must factor the equation. This will give you an answer of

f(x) = (x + 6) (x + 6)

Set each value in the parenthesis equal to 0, which will give you a result of

x = -6

To find the vertex, use the vertex equation

x = -b/(2a)

(a is the first coefficient, which is 1 in this case, and b is the second coefficient, which is 12 in this case).

This will give you an answer of

x = -6

To find the y value of the vertex, substitute the -6 in for x in the original equation. This will give you

f(x) = 0

Therefore, the vertex is (-6, 0). To graph, plot the intercepts and the vertex and connect the points in a parabola. (To find any additional points, choose any number to substitute in for x to find the y value.)