Calculate the coordinates of the turning point on the curve y = x^2 + 4x.
Thank you
To find the coordinates of the turning point on the curve y = x^2 + 4x, we need to determine the x-coordinate of the turning point, and then substitute that value back into the equation to find the corresponding y-coordinate.
Step 1: Rewrite the equation in vertex form
To find the vertex of a quadratic equation, we need to rewrite it in vertex form, which is given by:
y = a(x-h)^2 + k, where (h,k) represents the coordinates of the turning point.
Let's rewrite the equation y = x^2 + 4x in vertex form:
y = x^2 + 4x
= (x^2 + 4x + 4) - 4
= (x^2 + 4x + 4) - 4 + 4
= (x + 2)^2 - 4
So, the equation can be written as y = (x + 2)^2 - 4.
Step 2: Identify the vertex
From the vertex form (x + 2)^2 - 4, we can see that the vertex is given by (-2, -4).
Therefore, the turning point on the curve y = x^2 + 4x is (-2, -4).
To find the coordinates of the turning point on the curve y = x^2 + 4x, we need to find the vertex of the parabola.
The equation of a parabola in the form y = ax^2 + bx + c can be written as y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
In this case, a = 1, b = 4, and c = 0.
Let's complete the square to rewrite the equation in vertex form:
y = x^2 + 4x
= (x^2 + 4x + 4) - 4
= (x + 2)^2 - 4
From this form, we can see that the vertex is (-2, -4).
Therefore, the coordinates of the turning point on the curve y = x^2 + 4x are (-2, -4).
y = x(x+4)
The roots are at 0 and -4, so the vertex is at -2.
see http://www.wolframalpha.com/input/?i=x^2+%2B+4x