Where is the vertex of the graph of
y = x2 + 6x - 2?
Complete the square.
y = x2 + 6x - 2 = x^2 + 6x + 9 -11
= (x+3)^2 - 11
The lowest value of y occurs where x+3 = 0.
Solve for x and then y
To find the vertex of the graph of a quadratic function, you can follow these steps:
Step 1: Recall the vertex form of a quadratic function, which is given by y = a(x - h)^2 + k. In this form, (h, k) represents the coordinates of the vertex.
Step 2: Convert the given quadratic function, y = x^2 + 6x - 2, into the vertex form by completing the square.
y = x^2 + 6x - 2
To complete the square, add and subtract the square of half the coefficient of the x-term (which is (6/2)^2 = 9) inside the brackets:
y = x^2 + 6x + 9 - 9 - 2
Simplify the equation:
y = (x + 3)^2 - 11
Step 3: Now we can see that the vertex form of the quadratic function is y = (x + 3)^2 - 11. The vertex is given by the values of (h, k).
From the equation, we can see that h = -3 and k = -11.
Therefore, the vertex of the graph of y = x^2 + 6x - 2 is (-3, -11).