# Quadratic Function : Multiple Choice Questions

ဖုန်းဖြင့်ကြည့်သည့်အခါ စာများကို အပြည့်မမြင်ရလျှင် screen ကို ဘယ်ညာ ဆွဲကြည့်နိုင်ပါသည်။

# Important Notes

(Standard Form)
$f(x)=a x^{2}+b x+c, a \neq 0$
Graph Parabola
$a>0$ (opens upward)
$a<0$ (opens downward)
Axis of Symmetry $x=-\displaystyle\frac{b}{2 a}$
Vertex $\left(-\displaystyle\frac{b}{2 a}, f\left(-\displaystyle\frac{b}{2 a}\right)\right)=\left(-\displaystyle\frac{b}{2 a},-\displaystyle\frac{b^{2}-4 a c}{4 a}\right)$
y-intercept (0, c)
Discriminant $b^{2}-4 a c$
$b^{2}-4 a c>0 \Rightarrow$ two $x$ intercepts (cuts $x-$ axis at two points)
$b^{2}-4 a c=0 \Rightarrow$ one $x$ intercepts (touch $x$ -axis at one point $)$
$b^{2}-4 a c=0 \Rightarrow$ one $x$ intercepts (does not intersect $x$ -axis)
Quadratic Equation $a x^{2}+b x+c=0, a \neq 0$
Quadratic Formula $x=\displaystyle\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$
(Vertex Form)
$f(x)=a(x-h)^{2}+k, a \neq 0$
Vertex $(h, k)$
Axis of Symmetry
(Vertex Form)
$x=h$
(Intercept Form when
discriminant $>0$)
$f(x)=a(x-p)(x-q), a \neq 0$
$X$ -intercept points $(p, 0)$ and $(q, 0)$
Axis of Symmetry $x=\displaystyle\frac{p+q}{2}$
Quadratic Inequality $a x^{2}+b x+c>0$
$a x^{2}+b x+c \geq 0$
$a x^{2}+b x+c<0$
$a x^{2}+b x+c \leq 0$
$a>0$ and $b^2-4ac<0$

The graph does not cut the $x$ -axis.
$y<0 \Rightarrow$ solution set $=\varnothing$
$y=0 \Rightarrow$ solution set $=\varnothing$
$y>0 \Rightarrow$ solution set $=\mathbb{R}$
$a<0$ and $b^2-4ac<0$

The graph does not cut the $x$ -axis.
$y<0 \Rightarrow$ solution set $=\mathbb{R}$
$y=0 \Rightarrow$ solution set $=\varnothing$
$y>0 \Rightarrow$ solution set $=\varnothing$
$a>0$ and $b^2-4ac=0$

The graph touches the $x$ -axis.
$y<0 \Rightarrow$ solution set $=\varnothing$
$y=0 \Rightarrow$ solution set $=\left\{-\displaystyle\frac{b}{2 a}\right\}$
$y>0 \Rightarrow$ solution set $=\mathbb{R} \backslash\left\{-\displaystyle\frac{b}{2 a}\right\}$
$a<0$ and $b^2-4ac=0$

The graph touches the $x$ -axis.
$y<0 \Rightarrow$ solution set $=\mathbb{R} \backslash\left\{-\displaystyle\frac{b}{2 a}\right\}$
$y=0 \Rightarrow$ solution set $=\left\{-\displaystyle\frac{b}{2 a}\right\}$
$y>0 \Rightarrow$ solution set $=\varnothing$
$a>0$ and $b^2-4ac>0$

The graph cuts the $x$ -axis at two points.
$y<0 \Rightarrow$ solution set $=\{x \mid p<x<q\}$
$y=0 \Rightarrow$ solution set $=\{p, q\}$
$y>0 \Rightarrow$ solution set $=\{x \mid x<p$ or $x>q\}$
$a<0$ and $b^2-4ac>0$

The graph cuts the $x$ -axis at two points.
$y<0 \Rightarrow$ solution set $=\{x \mid x<p$ or $x>q\}$
$y=0 \Rightarrow$ solution set $=\{p, q\}$
$y>0 \Rightarrow$ solution set $=\{x \mid p<x<q\}$

အထက်ဖော်ပြပါ quadratic function နှင့်ဆိုင်သော definitions နှင့် concepts များကိုသိရှိနားလည်ပြီးလျှင် အောက်ပါ MCQ များကို လေ့ကျင့် ဖြေဆိုနိုင်ပါပြီ။ ဖြေဆိုပြီးကြောင်း Submit လုပ်ပြီးလျှင် ရမှတ်နှင့် အဖြေမှန်ကိုပါ ပြပေးမည် ဖြစ်သည်။ ရှင်းလင်းချက်မပါဝင်ပါ။