MediumMathematicsHigh School (11–12)Functions and Calculus › Graphs of FunctionsNumerical

Describe how to get the graph of y = -3(x + 2)² + 4 from the graph of y = x².

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Describe how to get the graph of $y = -3(x + 2)^2 + 4$ from the graph of $y = x^2$ . Find its vertex, say whether it opens upward or downward, and find its range.

Need a reminder? The key ideaShow

$f(x - h) + k$ moves the graph $h$ right and $k$ up; $a\,f(x)$ stretches the heights; $f(-x)$ and $-f(x)$ reflect it. Even: $f(-x) = f(x)$ . Odd: $f(-x) = -f(x)$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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← Write f(x) = |x + 2| + |x - 3| without bars for (a) x < -2, (b) -2 ≤ x ≤ 3 and (c) x > 3.The point (3, 4) is on the graph of y = f(x). →

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Describe how to get the graph of y = -3(x + 2)² + 4 from the graph of y = x².

The worked solution

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