Example Card: Graphing a Quadratic Function
Graph quadratic functions in Grade 9 algebra by finding the vertex using x=-b/(2a), determining the axis of symmetry, plotting key points, and sketching the parabola's shape and direction.
Key Concepts
Let's transform this quadratic equation into a complete graph by finding its essential features. This example showcases how to graph a function in the form $y = ax^2 + bx + c$.
Example Problem.
Graph the function $y = 2x^2 + 8x + 5$.
Common Questions
What key features do you need to graph a quadratic function?
To graph y = ax² + bx + c, find: the vertex (turning point), the axis of symmetry (x = -b/2a), the y-intercept (set x = 0), and a few additional points. Also determine if the parabola opens up (a > 0) or down (a < 0).
How do you find the vertex of a quadratic function?
Compute x = -b/(2a) to find the x-coordinate of the vertex. Then substitute this value back into the equation to find the y-coordinate. The vertex represents the maximum or minimum point of the parabola.
How does the value of 'a' affect the shape of a parabola?
If a > 0, the parabola opens upward with a minimum vertex. If a < 0, it opens downward with a maximum vertex. Larger |a| values make the parabola narrower; smaller |a| values make it wider.