Step 1:
Write the quadratic equation
[tex]\text{y = x}^2\text{ - 4x - 21}[/tex]Step 2:
To find the vertex point, find x = -b/2a
[tex]\begin{gathered} \text{a = 1 , b = -4} \\ x\text{ = }\frac{-(-4)}{2\times1} \\ \text{x = }\frac{4}{2} \\ \text{x = 2} \end{gathered}[/tex]Step 3:
find the value of y for the corresponding value of x.
[tex]\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}[/tex]Step 4:
[tex]\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}[/tex]Final answer
The minimum value is -25