Find the range of following expression.
$x^{2} + 4 x + 9$

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Solution

Solution:
The given equation is a quadratic equation
Quadratic functions which are graphs of parabolas have a maximum or minimum, the vertex. This vertex determines the range values.
equation is in the from $A x^{2} + B x + C = 0$
vertex found as $(- \frac{B}{2 A}, f (- \frac{B}{2 A}))$
$- \frac{B}{2 A} = - \frac{4}{2} = - 2$
$f (- 2) = (- 2)^{2} + 4 (- 2) + 9 = 5$
vertex $(- 2, 5)$ The lowest y value is $5$
Range: $y \geq 3$ or interval notation $[5, \infty]$

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