# Quadratics

These resources may support the topic of Quadratics.

### Solving a Quadratic Equation in Sin(x)

These videos from Casio explain how to solve the equation:

6 cos2^{x} +7sinx = 8 for x between 0 and 4π radians.

The graphical calculator solution shows how a graphical calculator can be used to verify the solution.

### Finding the Points of Intersection of a Linear and a Quadratic

These videos from Casio explain how to find the points of intersection of a linear and a quadratic function by solving the equations simultaneously.

The graphical solution explains how to use the graphic calculator to verify answers by drawing the two functions and finding the coordinates of the intersections of the two graphs

### Sketching a Quadratic Function by Firstly Expressing It in Completed Square Form

Thesevideos from Casio explain how to sketch the function f(x) = x^{2} + 6x + 8 by firstly expressing the function in completed square form.

The graphical solution explains how to use the graphic calculator to draw the graph of y = f(x), how to check the value of the minimum point and how to check where the graph crosses the axes. The video explains how to alter the scale of the graph in order to show all the points of intersection and then how to locate the key points on the graph.

### Finding the Minimum Value and Sketching a Quadratic Function

These videos from Casio explain how to find the minimum value and sketch the curve of y = 4x^{2} + 12x + 10.

The graphical solution explains how to use the graphic calculator to draw the graph of y = 4x^{2} + 12x + 10, how to change the scale of the axes on the display, how to find the minimum value and the point of intersection of the graph with the y axis.

### Solving a Quadratic Inequality

These videos from Casio explain how to solve the quadratic inequality 3x^{2} – 10x ≥ 8 by forming, and finding the roots of, the quadratic equation 3x^{2} – 10x - 8 = 0.

The graphical solution explains how to use the graphic calculator to draw the graph of y = 3x^{2} – 10x - 8 and find the roots in order to solve the given inequality.

### Linking the Properties and Forms of Quadratic Equations C1

In this DfE Standards Unit resource, students identify different forms and properties of quadratic functions, connect quadratic functions with their graphs and properties, including

intersections with axes, maxima and minima.

### Quadratic Equations

This interactive resource, produced by the University of Leicester, is designed to enable students to explore what is meant by a quadratic equation, the meaning of the coefficients of a quadratic equation and to be able to solve quadratic equations.

An introduction page gives examples of where quadratic equations can be found which is useful for class discussion. There follows an explanation of the first task in which students have to investigate how changing the coefficients affect the graph.

The second activity requires students to change the values of a, b and c so that the green graph matches the blue graph on the screen.

The third activity asks students to form equations to match the paths shown on the screen.

The fourth activity explores the roots of a quadratic equation. This is followed by pages of notes explaining the nature of quadratic equations including the formula for solving quadratic equations, the determinant, factorising a quadratic and completing the square. The final exercise asks students to solve a series of quadratic equations.