| ဖုန်းဖြင့်ကြည့်သည့်အခါ စာများကို အပြည့်မမြင်ရလျှင် screen ကို ဘယ်ညာ ဆွဲကြည့်နိုင်ပါသည်။ |
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Important Notes
| Quadratic Function (Standard Form) | $f(x)=a x^{2}+b x+c, a \neq 0$ |
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| 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 | $x=\displaystyle\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ |
| Quadratic Function (Vertex Form) | $f(x)=a(x-h)^{2}+k, a \neq 0$ |
| Vertex | $(h, k)$ |
| Axis of Symmetry (Vertex Form) | $x=h$ |
| Quadratic Function (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။
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