Quadratic Equations & Graphs

What you'll learn

Solving quadratic equations by the quadratic formula and by completing the square, and reading roots, turning point, and gradient from a quadratic graph.

• The quadratic formula solves ANY quadratic equation, even ones that don't factorise
• Completing the square rewrites the equation as \((x+p)^2 + q = 0\)
• The discriminant \(b^2 - 4ac\) tells you how many real roots there are
• The roots are exactly where the graph crosses the x-axis, and the axis of symmetry lies midway between them
• The turning point can be read directly from completed-square form
• Estimate the gradient of a curve at a point by drawing a tangent