If (a,-3) is a point on the graph of y=x^2+4x, what is the value of a?

so far i have -3=x^2+4x

i can do the problem on my graphing calc but we can't use a graphing calc on the test so i need to know how to do it by hand. what do i do next?

your equation would be

-3 = a^2 + 4a
a^2 + 4a + 3 = 0
(a+1)(a+3) = 0
a = -1 or a = -3

To solve the equation -3 = x^2 + 4x by hand, you can follow these steps:

1. Begin with the equation: -3 = x^2 + 4x.

2. Rearrange the equation to bring all terms to one side to form a quadratic equation: x^2 + 4x + 3 = 0.

3. Notice that the quadratic equation can be factored: (x + 3)(x + 1) = 0.

4. Set each factor equal to zero and solve for x:
a) x + 3 = 0, so x = -3.
b) x + 1 = 0, so x = -1.

So, there are two potential values of x: -3 and -1.

However, we are looking for the value of "a" in the given point (a, -3). Since the y-coordinate is fixed at -3, the x-coordinate must be a. Therefore, the value of a is -3.

Hence, the value of "a" in the point (a, -3) is -3.

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