Question

Cool Down: Rewrite This Expression

A quadratic function is defined by the expression x² - 20x + 19.
Rewrite the expression in vertex form and give the coordinates of the vertex. Show your
reasoning.

Answer 1

Answer: Write properties of function:

vertex form:

vertex form:

vertex:

vertex:

Answer 2

To rewrite the quadratic function x² - 20x + 19 in vertex form, we complete the square to obtain (x - 10)² - 81. The vertex of the parabola is at the coordinates (10, -81).

Step-by-step explanation:

To rewrite the quadratic function x² - 20x + 19 in vertex form, we need to complete the square. The vertex form of a quadratic function is given by a(x - h)² + k, where (h, k) is the vertex of the parabola.

First, factor out the coefficient of x², which is 1 in our case (so no factoring is needed). Then, rewrite the quadratic and linear terms as a perfect square. To do this, take half of the coefficient of x, which is -20/2 = -10, and square it to get 100.

Add and subtract this number inside the parentheses to maintain the balance of the equation:
x² - 20x + 100 - 100 + 19

Next, group the perfect square trinomial and the constants:

(x - 10)² - 81

The vertex form of the function is now (x - 10)² - 81, which reveals the vertex to be at the coordinates (10, -81).