Power functions

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12345The quadratic formula

Exercises

Exercise 1

Given the quadratic function $f$ with $f (x) = x^{2} + 8 x - 20$ .

Write the function rule in a form that allows you to read off the vertex of the graph.

Now there are three ways to determine the x-intersects of the graph of $f$ . Do this first by using the function rule that you found in a.

Now also use the quadratic formula to determine the zeros.

Finally, you can also factorise the equation. This is easiest if you "see " the factorisation. Calculate the zeros in this manner.

Exercise 2

Use your graphing calculator to plot the graphs of $f (x) = 2 x^{2} - x + 1$ and $g (x) = 10 - 3 x$ in one figure.

Solve: $f (x) = g (x)$

Solve, rounding to three decimals : $f (x) > g (x)$

Exercise 3

Solve the following equations:

$x^{2} + 3 x + 13 = 0$

$\frac{1}{3} x^{2} + 10 x + 1 = 0$

$2 x^{2} - 5 x = x$

$2 x^{2} - 12 x = -18$

$x^{2} - 5 x + 10 = 0$

$x (x - 1) = 12$

$60 - x^{2} = 0$

$5 - \frac{1}{3} x^{2} = 1$

$x - 5 x^{2} = 3$

Exercise 4

You should now practise using the quadratic formula via Practicum.

You there use AlgebraKIT to check your own progress. Keep practising until you no longer make mistakes.

Exercise 5

Given the functions $f$ and $g$ with $f (x) = p x^{2} + 6 x + 2 p$ and $g (x) = 6 - x$ .

Given $p = 2$ , calculate the x-intersects and the vertex of the graph of $f$ .

For which values of $p$ does the graph of $f$ have exactly one point in common with the $x$ -axis?

For which values of $p$ does the graph of $f$ have three intersects with the $x$ -axis and the $y$ -axis?

For which values of $p$ do these functions intersect each other?