About this topic
Before you begin
Sketch lines, quadratics, power and exponential graphs from their features, and use tangents to estimate local gradients.
Learning goals
- Plot given integer coordinate pairs
- Draw a given integer-coefficient line on a stated interval
- Interpret and draw graphs of functions
- Find and interpret a graph gradient
- Read and plot ordered coordinate pairs
- Draw a given integer-coefficient quadratic on a stated interval
- Sketch a quadratic given in factored or completed-square form through its key points
- Find the gradient of a straight-line graph from points on it
- Read the turning point of a quadratic graph and whether it is a maximum or a minimum
- Estimate the gradient of a curve at a point by drawing a tangent
- Match a drawn graph to its power or exponential function from the shape and key points
Syllabus statements covered
- Cartesian coordinates in two dimensions
- Graph of a set of ordered pairs as a representation of a relationship between two variables
- Linear functions (y = ax + b) and quadratic functions (y = ax² + bx + c)
- Graphs of linear functions
- The gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)
- Graphs of quadratic functions and their properties: - positive or negative coefficient of x^2 - maximum and minimum points - symmetry
- Sketching the graphs of quadratic functions given in the form: - y = (x − p)² + q - y = − (x − p)² + q - y = (x − a)(x − b) - y = − (x − a)(x − b)
- Graphs of power functions of the form y = ax^n, where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these
- Graphs of exponential functions y = ka^x, where a is a positive integer
- Estimation of the gradient of a curve by drawing a tangent
- Cartesian coordinates in two dimensions
- Graph of a set of ordered pairs as a representation of a relationship between two variables
- Linear functions y = ax + b
- Graphs of linear functions
- The gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)
- Quadratic functions y = ax^2 + bx + c
- Graphs of quadratic functions and their properties:
- Positive or negative coefficient of x^2
- Maximum and minimum points
- Symmetry
- Sketching the graphs of quadratic functions given in the form:
- y = (x − p)² + q
- y = −(x − p)² + q
- y = (x − a)(x − b)
- y = −(x − a)(x − b)
- Graphs of power functions y = ax^n , where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these
- Graphs of exponential functions y = ka^x , where a is a positive integer, a > 1
- Estimation of the gradient of a curve by drawing a tangent
Choose a lesson
Work through them in order.
- Not startedCoordinates, lines and gradientsNextPlot ordered pairs and read a straight line’s gradient from changes in the labelled coordinates.
- Not startedQuadratic graphs and turning pointsNextUse tables and symmetry to locate a quadratic curve’s roots and extremum.
- Not startedSketch quadratics from their formNextRead a vertex or roots from a suitable form and locate the remaining features before sketching.
- Not startedPower and exponential graphsNextUse domains, tables and asymptotes to distinguish power functions from exponential growth.
- Not startedEstimate a curve’s gradientNextDraw a tangent at the specified point and use two separated points on that tangent.
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