Question: Given that f(x) = x^2 + 6x - 5 and g(x) = 8x + k. Find the range of values of k for which f(x) > g(x).

How should I approach this question?

Thank you

2. ## Re: Quadratic function question

$x^2 + 6x - 5 > 8x + k\iff x^2 - 2x - (5+k) > 0$. Do you know how to determine if a quadratic polynomial has no roots?

Another way is to sketch the graphs of f(x) and g(x) and to understand that the line that is the graph of g(x) with the critical value of k is a tangent to the parabola that is the graph of f(x). Find the slope of f(x) (it depends on x) and equate it to the slope of g(x) (which is constant). From this equation, find x and y = f(x) and then find k such that g(x) passes through (x, y).

3. ## Re: Quadratic function question

Originally Posted by emakarov
$x^2 + 6x - 5 > 8x + k\iff x^2 - 2x - (5+k) > 0$. Do you know how to determine if a quadratic polynomial has no roots?

Another way is to sketch the graphs of f(x) and g(x) and to understand that the line that is the graph of g(x) with the critical value of k is a tangent to the parabola that is the graph of f(x). Find the slope of f(x) (it depends on x) and equate it to the slope of g(x) (which is constant). From this equation, find x and y = f(x) and then find k such that g(x) passes through (x, y).
I managed to answer the question correctly. =) You can mark this as solved now, thank you so much!