the standard form of the equation of a parabola is y=x^2-6x+14.what is the vertex form of the equation?
To convert the standard form of a quadratic equation into vertex form, also known as the completed square form, you need to follow a few steps. The vertex form of a parabola is written as y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.
Step 1: Identify the values of a, b, and c in the standard form equation, y = ax^2 + bx + c. In this case, a = 1, b = -6, and c = 14.
Step 2: Use the formula x = -b/2a to find the x-coordinate of the vertex. Calculate the x-value by substituting the values of a and b into the formula: x = -(-6) / (2 * 1) = 6 / 2 = 3.
Step 3: Substitute the x-coordinate of the vertex, which is 3, back into the original equation to find the y-value. Calculate y by substituting the values of x and a into the equation: y = (3)^2 - 6(3) + 14 = 9 - 18 + 14 = 5.
Step 4: Rewrite the equation using the vertex coordinates (h, k) which are (3, 5). The equation in vertex form is: y = 1(x - 3)^2 + 5.
So, the vertex form of the equation y = x^2 - 6x + 14 is y = (x - 3)^2 + 5.
x^2 +6x+9 + 5
(x+3)^2 + 5