Study notes
Quadratic Equations & Graphs
Solving quadratic equations by the quadratic formula and by completing the square, and reading roots, turning point, and gradient from a quadratic graph.
What this topic covers
- 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
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