using completing the square find the vertex and axis of symmetry for
y = x^2 - 6x + 7
i cant complete the square for this one please help??
To find the vertex and axis of symmetry of the given quadratic equation, we can use the completing the square method.
Step 1: Start with the given equation in the form y = ax^2 + bx + c. Rewrite the equation, leaving space to complete the square:
y = x^2 - 6x + 7
Step 2: To complete the square, we need to add a constant term to both sides of the equation, which is half the coefficient of x, squared.
In this case, the coefficient of x is -6. Half of -6 is -3, and (-3)^2 is 9. So we will add 9 to both sides of the equation:
y + 9 = x^2 - 6x + 9 + 7
Step 3: The next step is to factor the perfect square trinomial on the right side of the equation. We then simplify and combine like terms:
y + 9 = (x - 3)^2 + 16
Step 4: Now, we can rewrite the equation in vertex form by isolating the y variable:
y = (x - 3)^2 + 16 - 9
y = (x - 3)^2 + 7
Step 5: Comparing this equation with y = a(x - h)^2 + k, we can identify the vertex and axis of symmetry:
The vertex of the parabola is (h, k), where h is the x-coordinate and k is the y-coordinate.
In this case, the vertex is (3, 7).
The equation of the axis of symmetry is given by x = h.
Therefore, the axis of symmetry is x = 3.
So, the vertex of the parabola is (3, 7), and the axis of symmetry is x = 3.