Cubic Graph Sketching start considering the \(x\)-intercepts and whether the leading coefficient is either positive or negative.
Question 1
Sketch the graph of \( y=(x-1)(x+2)(x-3) \).
The graph cuts at \( x=1, x=-2, x=3 \).
Question 2
Sketch the graph of \( y=(x^2-2x)(x+3) \).
\( y=(x^2-2x)(x+3) = x(x-2)(x+3) \)
The graph cuts at \( x=0, x=2, x=-3 \).
Question 3
Sketch the graph of \( y=(x+1)(x-2)^2 \).
The graph cuts at \( x=-1 \) and touches \( x=2 \).
Question 4
Sketch the graph of \( y=(x+1)^2(x-2) \).
The graph touches at \( x=-1 \) and cuts \( x=2 \).
Question 5
Sketch the graph of \( y=x^2(x+2) \).
The graph touches at \( x=0 \) and cuts \( x=-2 \).
Question 6
Sketch the graph of \( y=x(x+2)^2 \).
The graph touches at \( x=-2 \) and cuts \( x=0 \).
Question 7
Sketch the graph of \( y=-x^2(x-2) \).
The graph touches at \( x=0 \) and cuts \( x=2 \).
Question 8
Sketch the graph of \( y=(x+1)^2(2-x) \).
\( y=(x+1)^2(2-x) = -(x+1)^2(x-2)\)
The graph touches at \( x=-1 \) and cuts \( x=2 \).
Algebra Algebraic Fractions Arc Binomial Expansion Capacity Common Difference Common Ratio Differentiation Double-Angle Formula Equation Exponent Exponential Function Factorials Factorise Functions Geometric Sequence Geometric Series Index Laws Inequality Integration Kinematics Length Conversion Logarithm Logarithmic Functions Mass Conversion Mathematical Induction Measurement Perfect Square Perimeter Prime Factorisation Probability Product Rule Proof Quadratic Quadratic Factorise Ratio Rational Functions Sequence Sketching Graphs Surds Time Transformation Trigonometric Functions Trigonometric Properties Volume
