Connecting Quadratic Equations to Parabola Functions

Q: What does this topic cover at Standard?

Covers graphing parabolas and working with the three useful forms of a quadratic: standard form y = ax^2 + bx + c, vertex form y = a(x - h)^2 + k, and factored form y = a(x - p)(x - q). You identify the vertex, axis of symmetry x = -b/(2a), y-intercept, and roots, then sketch accurate parabolas. Sits in Unit 3 Standard as the step beyond linear functions, building algebra and graphing fluency for 2-D quadratic applications.

Q: Common mistake finding the vertex?

Students often forget the negative sign in x = -b/(2a) or substitute b without its sign. For y = 2x^2 - 8x + 3, b is -8, so x = -(-8)/(2*2) = 2. Once you have the x-coordinate, plug it back into the original equation to get y; don't stop at x. Check the sign of a: positive means a minimum at the vertex, negative means a maximum. Labelling the vertex as a coordinate pair (h, k) earns the mark.

Connect quadratic equations to parabola graphs in MYP Year 5 Maths. Learn vertex, roots, axis of symmetry and how to sketch quadratic functions for MYP assessments.

Practice

Quadratic Equations & Functions

180 min0 marks

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From Equation to Graph

A quadratic function takes the form f(x) = ax² + bx + c and produces a U-shaped curve called a parabola. This topic is about understanding the connection between solving a quadratic equation and reading key features from its graph. In MYP Year 5, you need to move fluently between the algebraic and graphical representations.

Key Features of a Parabola

The Vertex

The vertex is the turning point of the parabola — the minimum point if a > 0 (opens upward) or the maximum if a < 0 (opens downward). The x-coordinate of the vertex is found using x = −b / 2a. Substitute this back into the function to find the y-coordinate. When you complete the square to get f(x) = a(x + p)² + q, the vertex is simply (−p, q).

The Roots (x-intercepts)

The roots are where the parabola crosses the x-axis — these are the solutions to f(x) = 0. There may be two, one (a tangent to the x-axis), or zero real roots, depending on the discriminant. Solving the quadratic equation gives you these graphically meaningful points.

The y-intercept

Set x = 0: f(0) = c. This is always the y-intercept and is easy to read directly from the standard form equation.

The Axis of Symmetry

The parabola is symmetric about a vertical line through the vertex: x = −b / 2a. Marking this on your graph shows understanding of the function's structure.

Common Mistakes

Assuming all parabolas open upward — check the sign of a.
Plotting roots correctly but placing the vertex in the wrong position.
Not labelling the axis of symmetry when asked to sketch the function.

How to Practise

For each quadratic function you study: identify a, b, c; calculate the discriminant; find the roots; find the vertex; sketch the graph with all key features labelled. This systematic approach works well for both Criterion A and Criterion C tasks.

Frequently asked questions