investigation
For the following quadratic functions, use a graphing program
- Geogebra sample parabola
- Desmos sample parabola
- the one on this site function plotter
or any other function plotter) to:
- draw the graph
- find the y-intercept
- find the x-intercepts (if there are any)
${y = x^2 - 3x - 4}$
${y = -x^2 + 2x + 8}$${y = 2x^2 - 3x}$${y = -x^2 + 2x - 3}$${y = (x - 1)(x - 3)}$${y = -(x + 2)(x - 3)}$${y = 3(x + 1)(x + 4)}$${y = 2(x - 2)^2}$${y = -3(x + 1)^2}$
From what you notice in part 1.
- state what the y-intercept is for
${y = ax^2 + bx + c}$ - state what the x-intercept is for
${y = a(x - \alpha)(x - \beta)}$ - what can you say about the x-intercepts for
${y = a(x - \alpha)^2}$?
idea from Haese & Harris