Geometric Bites

Parabolas in sight: The Clifton Suspension Bridge, Bristol, United Kingdom. A quadratic function is a function whose graph is a parabola (a U-shaped curve). One of the most useful ways to write a quadratic is in vertex form , because it shows the parabola’s turning point immediately. 1) The vertex form A quadratic function in vertex form is written as: f(x) = a(x - h) 2 + k This form is especially helpful because the values h and k tell you the vertex directly. 2) The vertex (turning point) The vertex is the point where the parabola changes direction. In vertex form: Vertex = (h, k) If the parabola opens up , the vertex is the lowest point (a minimum). If the parabola opens down , the vertex is the highest point (a maximum). 3) What the number a does The number a controls two key things: the direction the parabola opens, and how wide or narrow it is. a > 0 means the parabola opens up (U-shape). a < 0 means the parabola opens dow...

Below are the workings required to build an interactive graph that finds the points where a line and quadratic equation intersect . Here 'a' is not equal to 0 as it becomes part of the denominator a fraction . Also, if 'a' were equal to 0, we'd have a line intersecting a line, not a parabola (for instance). When we have the formula for 'x', we just plug it back into the linear equation to get the outcomes for 'y'. And there we have it, the points where a line and quadratic equation intersect. To see the interactive graph I was talking about, visit the Desmos link below: https://www.desmos.com/calculator/sqzjajbhea