Quadratic functions with absolute value
Which equation belongs to the graph in the picture?
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Absolute value changes the graph of a parabola in two ways. For y = |x² − 4x + 3| the part of the parabola below the x-axis is reflected upwards. For y = x² − 4|x| + 3 you draw only the right half of the parabola (x ≥ 0) and mirror it in the y-axis to the left. The number of solutions of f(x) = c can then be read from the graph: it is the number of points where the horizontal line y = c meets it.
What does this generator do?
On the easy level it draws a graph and offers four equations: the plain parabola, |g(x)|, g(|x|) and |g(|x|)|. On the medium level the graph is shown next to the equation and you find how many solutions f(x) = c has. On the hard level you only get the equation and sketch the graph yourself.
How to use it
1) First draw the parabola without absolute value: vertex and x-intercepts. 2) For |g(x)| reflect the part below the x-axis upwards. 3) For g(|x|) keep only the part to the right of the y-axis and mirror it to the left. 4) Draw the horizontal line y = c and count the intersections. Careful: touching the graph at a turning point counts as one intersection.