# Sketching Quadratic Graphs

Sketching quadratic graphs are drawn based on \( y=x^2 \) graph for transforming and translating.

## Question 1

\(f(x) = (x-3)^2 \) is drawn and sketch the following graphs by transforming.

(a) \( y = f(x)+2 \); Transforming upwards by \( 2 \) units

(b) \( y=f(x)-3 \); Transforming dowanwards by \( 3 \) units

(c) \(y=-f(x)\); Rotating by \(x\)-axis

(d) \(y=f(-x)\); Rotating by \(y\)-axis

(e) \(y=f(x+2)\); Transforming to the left by \( 2 \) units

(f) \(y=f(x-1)\); Transforming to the right by \( 1 \) unit

(g) \(y=f(x+4)-5\); Transforming to the left by \( 4 \) units and downwards by \( 5 \) units

(h) \(y=-f(x+2)\); Rotating to \(x\)-axis, then transforming to the left by \( 2 \) units

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

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

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

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

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

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

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

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

## Question 2

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

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

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

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

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

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

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

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

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