How do you find the vertex and x intercept of #f(x)=x^2+11x+30#?

1 Answer
Nghi N.
Aug 3, 2016

Vertex #(-11/2, -1/4)#
x-intercepts: -5 and -6

Explanation:

#f(x) = x^2 + 11x + 30.#
x-coordinate of vertex:
#x = -b/(2a) = - 11/2#
y-coordinate of vertex:
#y(-11/2) = 121/4 - 121/2 + 30 = -121/4 + 120/4 = - 1/4#
Vertex #(-11/2, -1/4)#
To find the 2 x-intercepts, solve the quadratic equation f(x) = 0.
Find 2 real roots, knowing sum (-b = -11) and product (c = 30).
The 2 x-intercepts are: - 5 and -6 -> sum (- 11 = -b) --> product (30).

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