IB Maths AA HL AA 2.2 Quadratics questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper

Paper 1, no calculator Paper 2, calculator

Difficulty

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Question 1

Paper 1, no calculatorMedium6 marks

For real $p$ consider the equation

x^2-2px+p+2=0,\qquad x\in\mathbb R.

(a)

Determine the values of $p$ for which the equation has (i) two distinct real roots, (ii) two equal real roots, and (iii) no real roots.

[4]

(b)

Hence, when $p=3$ solve

x^2-2px+p+2\leq 0.

[2]

Question 2

Paper 1, no calculatorHard6 marks

A non-constant quadratic function $f$ satisfies $f(x)=f(4-x)$ for every real $x$ It is also known that $f(4)=-2$ and $f(2)=6$

(a)

Determine $f(0)$

[1]

(b)

Determine $f(x)$ in vertex form.

[2]

(c)

Hence determine all real values of $m$ for which the line $y=mx$ intersects the graph of $y=f(x)$ at two distinct points.

[3]

Question 3

Paper 1, no calculatorHard6 marks

Figure 1 shows the graph of a quadratic function $f$ The marked points lie exactly on grid intersections.

(a)

Determine $f(x)$ in factorized form.

[2]

(b)

A quadratic function $g$ has the same $x$ -intercepts as $f$ The $y$ -coordinate of the vertex of $g$ is equal to the $y$ -intercept of $f$

Determine $g(x)$ in the form $a(x-h)^2+k$

[4]

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