how do you solve f(x)= G(X)
and find the points of intersection of the graphs of the 2 functions
f(x)= x^2 + 5x+ 13
g(x)= 19
set x^2 + 5x + 13 = 19
x^2 + 5x - 6=0
(x+6)(x-1) = 0
x = -6 or x=1
To solve the equation f(x) = g(x), you need to find the values of x for which f(x) and g(x) are equal. In this case, you have the following functions:
f(x) = x^2 + 5x + 13
g(x) = 19
To solve f(x) = g(x), you need to set the two equations equal to each other and solve for x:
x^2 + 5x + 13 = 19
To solve this quadratic equation, you can start by subtracting 19 from both sides:
x^2 + 5x + 13 - 19 = 0
Simplifying further:
x^2 + 5x - 6 = 0
Next, you can try factoring the quadratic equation:
(x + 6)(x - 1) = 0
Now, you can set each factor equal to zero and solve for x:
x + 6 = 0, or x - 1 = 0
Solving for x in each equation gives you:
x = -6, or x = 1
The points of intersection of the graphs of the two functions f(x) and g(x) correspond to the x-values where the two functions are equal. In this case, the points of intersection are (-6, 19) and (1, 19), where the y-value is 19 for both functions.