To find the solutions to the system of equations y = x^2 + 6x + 8 and y = x + 4, we can graph the two equations on the same coordinate plane and see where they intersect.
First, let's graph the equation y = x^2 + 6x + 8. We can rewrite this equation in vertex form by completing the square:
y = x^2 + 6x + 8
= (x^2 + 6x + 9) + 8 - 9
= (x + 3)^2 - 1
This equation represents a parabola that opens upwards and is shifted 3 units to the left and 1 unit downward. The vertex of this parabola is (-3, -1).
Next, let's graph the equation y = x + 4. This equation represents a straight line with a slope of 1 and a y-intercept of 4. Since the coefficient of x is 1, the line has a slope of 1, meaning it goes up 1 unit for every 1 unit to the right.
Now, let's plot the vertex (-3, -1) of the parabola and draw the parabola. Then, let's plot the y-intercept (0, 4) of the line and draw the line. The graph should look like this:
graph(200,200,-10,10,-10,10,x^2 + 6x + 8, x + 4)
From the graph, it's clear that the two equations intersect at a point (-2, 2). Therefore, the solution to the system of equations is x = -2 and y = 2.
Use graphing to find the solutions to the system of equations.
y=x^2+6x+8
y=x+4
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