If (a,-12) is a point on the graph of y=x^2+7x, what is a?
please show work
To find the value of 'a,' we can substitute the given point (a, -12) into the equation of the graph, y = x^2 + 7x, and solve for 'a.' Here's how you can do it step-by-step:
1. Substitute the values of x and y from the given point into the equation:
-12 = a^2 + 7a
2. Rearrange the equation to set it equal to zero:
a^2 + 7a + 12 = 0
3. Factorize the quadratic equation:
(a + 3)(a + 4) = 0
Using the zero-product property, we set each factor equal to zero:
a + 3 = 0 or a + 4 = 0
4. Solve for 'a' in both equations:
For a + 3 = 0: a = -3
For a + 4 = 0: a = -4
So, there are two possible values of 'a' that satisfy the given point: a = -3 or a = -4.