Analysing Transformed Quadratic Functions

≈ 35 min

Analysing Transformed Quadratic Functions

A transformed quadratic $y=a(x-p)^2+q$ shows its turning point $(p,q)$ directly. The sign of $a$ tells whether it opens up or down; its size controls steepness. For exam questions, connect equation, graph and features: intercepts, axis of symmetry, range, increasing/decreasing intervals and maximum or minimum.

Worked reasoning

For $y=-2(x-1)^2+8$ , turning point is $(1,8)$ , axis is $x=1$ , and it opens downward. Its maximum value is 8.

Exam method

Identify vertex form. 2. Read p, q and a. 3. Find intercepts if required and write features using correct coordinate/interval notation.

Feature checklist for a parabola

When a quadratic graph is supplied or requested, work through a fixed checklist: opening, turning point, axis, x-intercepts, y-intercept, range and intervals of increase/decrease. Use coordinate notation for points and inequality/interval language for ranges. If roots are irrational, label their approximate locations but keep exact values when the question asks for algebra. The checklist turns a complex graph question into a sequence of markable observations.

One-minute retrieval: Analysing Transformed Quadratic Functions

Close the worked solution. From memory, state its central rule, name one condition that makes it valid, and reconstruct one check that would catch a typical exam error.

Give the turning point of $y=(x+3)^2-2$ .

For $y=-x^2+4$ , what is the maximum y-value?

For $y=3(x-2)^2+1$ , the axis of symmetry is:

$x=2$

$y=2$

$x=-2$

$y=1$

Find $y$ when $x=0$ for $y=(x-2)^2-3$ .