Answer: see below
Step-by-step explanation:
Given ax² + bx + c = 0
If a > 0 (positive), then parabola opens UP
If a < 0 (negative), then parabola opens (DOWN)
Axis of Symmetry: [tex]x=\dfrac{-b}{2a}[/tex]
Max/Min: Plug axis of symmetry into the given equation and solve for y.
1) y = x² + 11x + 24
a=1 b=11
a> 0 so parabola opens UP
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(11)}{2(1)}=\dfrac{-11}{2}=-3.5\\\\\\\text{Minimum:}\quad y=(-3.5)^2+11(-3.5)+24 = -6.25[/tex]
2) y = -x² - 6x - 8
a=-1 b=-6
a< 0 so parabola opens DOWN
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(-6)}{2(-1)}=\dfrac{6}{-2}=-3\\\\\\\text{Maximum:}\quad y=(-3)^2-6(-3)-8 = 1[/tex]
3) y = x² - 2x + 3
a=1 b=-2
a> 0 so parabola opens UP
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(-2)}{2(1)}=\dfrac{2}{2}=1\\\\\\\text{Minimum:}\quad y=(1)^2-2(1)+3 = 2[/tex]
4) y = x² + 4x + 4
a=1 b=4
a> 0 so parabola opens UP
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(4)}{2(1)}=\dfrac{-4}{2}=-2\\\\\\\text{Minimum:}\quad y=(-2)^2+4(-2)+4 = 0[/tex]
5) y = 3x² + 21x + 30
a=3 b=21
a> 0 so parabola opens UP
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(21)}{2(3)}=\dfrac{-21}{6}=-3.5\\\\\\\text{Minimum:}\quad y=3(-3.5)^2+21(-3.5)+30 = -6.75[/tex]
