Question

Use completing the square to rewrite y = x2 − 4x − 21 in vertex form. Identify the maximum or minimum value.

Answer 1

Step 1:

Write the quadratic equation

`\text{y = x}^2\text{ - 4x - 21}`

Step 2:

To find the vertex point, find x = -b/2a

`\begin{gathered} \text{a = 1 , b = -4} \\ x\text{ = }(-(-4))/(2*1) \\ \text{x = }(4)/(2) \\ \text{x = 2} \end{gathered}`

Step 3:

find the value of y for the corresponding value of x.

`\begin{gathered} \text{y = x}^2\text{ - 4x - 21} \\ y=2^2\text{ - 4(2) - 21} \\ \text{y = 4 - 8 - 21} \\ \text{y = -25} \end{gathered}`

Step 4:

`\begin{gathered} \text{From ax}^2\text{ + bx + c = 0} \\ \text{Compare with x}^2\text{ - 4x - 21 = 0} \\ \text{If a > 0 (positive) then the vertex is minimum} \\ \text{if a < 0 (negative) then the vertex is maxi}mim \\ \text{Hence, from the equation a >0, them the vertex is minimum.} \end{gathered}`

Final answer

The minimum value is -25