Sketching Quadratic Graphs

Sketching Quadratic Graphs using Transfomration

Sketching Quadratic Graphs are drawn based on \( y=x^2 \) graph for transforming and translating.
\(y = (x-3)^2 \) is drawn and sketch the following graphs by transforming.

\(f(x)=(x-3)^2\)

Quadratic Graphs Q01

\(y=f(x)+2\)

Transforming upwards by 2 units

\(y=f(x)-3\)

Transforming dowanwards by 3 units

\(y=-f(x)\)

Rotating by \(x\)-axis

\(y=f(-x)\)

Rotating by \(y\)-axis

\(y=f(x+2)\)

Transforming to the left by 2 units

\(y=f(x-1)\)

Transforming to the right by 1 unit

\(y=f(x+4)-5\)

Transforming to the left by 4 units and downwards by 5 units

\(y=-f(x+2)\)

Rotating to \(x\)-axis, then transforming to the left by 2 units

\(y=2f(x)\)

\( \displaystyle y=\frac{1}{2}f(x)\)

\(y=-4f(x)\)

\(y=3f(x+5)\)

\(y=-f(x+6)-3\)

\(y=2f(x)-4\)

\(y=-2f(x+3)+1\)

\(y=2f(-x)-2\)

\(y=(x-1)^2\)

\(y=(x+2)^2\)

\(y=(x+5)^2-3\)

\(y=(x-4)^2+3\)

\(y=-(x+2)^2\)

\(y=-(x-3)^2\)

\(y=-(x-3)^2+2\)

\(y=-(x+4)^2-2\)