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.

Quadratic-Graph-Q1

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

Quadratic-Graph-Q1a

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

Quadratic-Graph-Q1b

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

Quadratic-Graph-Q1c

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

Quadratic-Graph-Q1d

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

Quadratic-Graph-Q1e

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

Quadratic-Graph-Q1f

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

Quadratic-Graph-Q1g

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

Quadratic-Graph-Q1h

(i)   \(y=2f(x)\)

Quadratic-Graph-Q1i

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

Quadratic-Graph-Q1j

(k)   \(y=-4f(x)\)

Quadratic-Graph-Q1k

(l)   \(y=3f(x+5)\)

Quadratic-Graph-Q1l

(m)   \(y=-f(x+6)-3\)

Quadratic-Graph-Q1m

(n)   \(y=2f(x)-4\)

Quadratic-Graph-Q1n

(o)   \(y=-2f(x+3)+1\)

Quadratic-Graph-Q1o

(p)   \(y=2f(-x)-2\)

Quadratic-Graph-Q1p

Question 2

(a)   \(y=(x-1)^2\)

Quadratic-Graph-Q2a

(b)   \(y=(x+2)^2\)

Quadratic-Graph-Q2b

(c)   \(y=(x+5)^2-3\)

Quadratic-Graph-Q2c

(d)   \(y=(x-4)^2+3\)

Quadratic-Graph-Q2d

(e)   \(y=-(x+2)^2\)

Quadratic-Graph-Q2e

(f)   \(y=-(x-3)^2\)

Quadratic-Graph-Q2f

(g)   \(y=-(x-3)^2+2\)

Quadratic-Graph-Q2g

(h)   \(y=-(x+4)^2-2\)

Quadratic-Graph-Q2h

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