Put the quadratics below into vertex form by completing the square. state the vertex.
a) y=x^2 - 4x-21
y=x^2 - 4x-21
= (x^2 - 4x + 4 - 4) - 21
= ( (x-2)^2 - 4) - 21
= (x-2)^2 - 4 - 21
= (x-2)^2 - 25
take over
To put the given quadratic equation y = x^2 - 4x - 21 into vertex form by completing the square, follow these steps:
Step 1: Group the x-terms together and isolate the constant term (if necessary).
y = (x^2 - 4x) - 21
Step 2: Complete the square for the x-terms by adding and subtracting the square of half the coefficient of x (4/2)^2 = 4.
y = (x^2 - 4x + 4 - 4) - 21
Step 3: Factor the square of half the coefficient of x and combine it with the constant term inside the square brackets.
y = (x^2 - 4x + 4) - 4 - 21
Step 4: Simplify inside the brackets by factoring as a perfect square trinomial.
y = (x - 2)^2 - 25
The equation is now in vertex form: y = (x - h)^2 + k, where the vertex is represented by the coordinates (h, k). In this case, the vertex is (2, -25).