# How to graph a Quadratic equation.

I have an equation that goes: $0.0001x^2 - 0.22x + 197$. I'm not asking for the answer, but instead, how can I graph it without dealing with these insanely tough numbers.

• It is an upward facing parabola with vertex $1100$ and y intercept $197$. That should suffice for getting started. – Macavity Mar 3 '16 at 5:10
• Define $X=\frac{x}{100}$ or $x=100 X$ and you will get rid of these insanely tough numbers (as you said). – Claude Leibovici Mar 3 '16 at 5:11
• @ClaudeLeibovici, Strange!, graphing $y=\frac{(x-1100)^2}{10000}+76$ and the expression in the question both produce different graphs when they both are equivalent – Vikram Mar 3 '16 at 5:52
• @Vikram. How did you get different graphs ? This does not seem possible. By the way, your expression is nice. – Claude Leibovici Mar 3 '16 at 6:00
• @ClaudeLeibovici, thanx, desmos did not refresh :), they both produce the same graph – Vikram Mar 3 '16 at 6:05

As suggested by Claude Leibovici, you can define $x=100X$. Then you have
$$\begin{array}{ll} 0.0001x^2−0.22x+197 &= 0.0001\cdot (100X)^2−0.22\cdot 100X+197 \\ & = X^2+22X+197\end{array}$$