Question

How do I find the parabola of the following. I tried to start. I do not know if I am on the right track, and if I am on the right track, what are the next steps to find and plot the parabola?

Thank you,

(x+4)(x+2)=0
((x+2)+4(x+2)
x^2 +2x+4x+8
X^2+6x+8

Answer 1

You are on the right track! To find the equation of the parabola given by the equation x^2 + 6x + 8 = 0, you can use the standard form of a quadratic equation, which is:

• y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the parabola.

To get the equation of your parabola, you first need to complete the square on the x terms of the given equation:

• x^2 + 6x + 8 = 0
• x^2 + 6x = -8
• (x + 3)^2 - 9 = -8
• (x + 3)^2 = 1

From this equation, you can see that the vertex of the parabola is at (-3, -1) and the value of a is positive. This means that the parabola opens upwards.

To find the value of a, you can compare the equation with the standard form of the quadratic equation:

• y = a(x - h)^2 + k

where h = -3, k = -1, and a is the coefficient you need to find. Substituting these values into the equation gives:

• -1 = a(-3 - (-3))^2 - 1
• -1 = a(0)^2 - 1
• a = 1

So the equation of the parabola is:

• y = (x + 3)^2 - 1

To plot the parabola, you can use the vertex (-3, -1) as a starting point and then use the coefficient a to determine the shape of the parabola. Since a is positive, the parabola opens upwards.