Where is the graph of f(x)= x^2-10x-6 increasing?

Question

it says the answer is x< -5 but I'm confused about exactly how they got there

Answer 1

x^2 -10x-6

a=1 b=-10 c=-6finding vertex formula -b/2a then plug values

-(-10)/2(1)

=5

plug -5 in the quadratic equation we get -

(5)^2 -10(-5) -6

25+50-6

69

(5,69)

so the graph is increasing.

Answer 2

This is an upward opening parabola because the coefficient of x² is positive. Do you know how to find the vertex? The function will be increasing from the x-coordinate of the vertex to positive infinity. That means as x increases the corresponding y-values increase too.

There are two basic ways to find the vertex. Since all this problem cares about is the x-coordinate of the vertex , let's use the method that the axis of symmetry is given by the equation x = -b / 2a where b = -10 and a = 1.

So x = -(-10) / 2(1) = 10 / 2 = 5. If we had to find the y-coordinate too plug 5 into the function, i.e. find f(5).

Since the vertex lies on the axis of symmetry the function is increasing from 5 to +∞.

Take a look at the following graph and notice the part of the parabola that is falling as x gets larger and the part that is rising as x gets larger. Also take a look at the table. Before 5, as x gets larger the y-values are getting smaller. After 5, as x gets larger, y-values are getting bigger.

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