Write the following expression in vertex form by completing the square
y= 𝑥2 − 12𝑥 + 7.
To complete the square, we need to take half of the coefficient of x, square it, and add it to both sides of the equation.
First, let's factor out the leading coefficient of 1:
y = 1(𝑥2 - 12𝑥) + 7
To complete the square, we need to add (12/2)^2 = 36 to both sides:
y = 1(𝑥2 - 12𝑥 + 36) - 36 + 7
y = 1(𝑥 - 6)2 - 29
So the vertex form of the equation is:
y = (𝑥 - 6)2 - 29
Therefore, the vertex is at (6, -29) and the parabola opens upwards.
To write the expression in vertex form, we need to complete the square.
Step 1: First, we take the coefficient of the linear term (in this case, -12) and divide it by 2, then square the result.
(-12/2)² = (-6)² = 36
Step 2: Add the result from Step 1 to the expression inside the parentheses to make it a perfect square
y = x² - 12x + 7 + 36
Step 3: Rewrite the expression by factoring the perfect square trinomial
y = (x² - 12x + 36) + 7
Step 4: Simplify the expression inside the parentheses
y = (x - 6)² + 7
So, the expression y = x² - 12x + 7 can be written in vertex form as y = (x - 6)² + 7.