Find the axis of symmetry and the vertex and graph the following: f(x)=(x+2)(x-4)

1 answer:

8 0

something noteworthy is that the independent and squared variable in this case will be the "x", namely the graph of that quadratic is a vertical parabola.

$\bf f(x) = (x+2)(x-4)\implies 0=(x+2)(x-4)\implies x = \begin{cases} -2\\ 4 \end{cases} \\\\\\ \boxed{-2}\rule[0.35em]{7em}{0.25pt}0\rule[0.35em]{3em}{0.25pt}\stackrel{\downarrow }{1}\rule[0.35em]{10em}{0.25pt}\boxed{4}$

so the parabola has solutions at x = -2 and x = 4, and its vertex will be half-way between those two guys, namely at x = 1.

since this is a vertical parabola, its axis of symmetry, the line that splits its into twin sides, will be a vertical line, and it'll be the x-coordinate of the vertex, since the vertex hasa a coordinate of x = 1, then the axis of symmetry is the vertical line of x = 1.

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A spinner is divided into 4 sections. The spinner is spun 100 times. The probability distribution shows the results.

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P(1≤x≤3) defined the probability that the result is between 1 and 3, included. You can answer this question in two ways:

1. Sum the probabilities of good events:

From the graph, we have

$P(x=1) = 0.32,\quad P(x=2) = 0.24,\quad P(x=3) = 0.28$

So,

$P(1\leq x \leq 3) = 0.32+0.24+0.28 = 0.84$

2. Use complementary probabilities

Asking that the result is 1, 2 or 3 is the same as asking that the result is not 4. The probability that the result is 4 is 0.16, so the probability that the result is not 4 will be

$P(x\neq 4) = 1-P(x=4) = 1-0.16=0.84$