How do you determine whether the graph of $y = - 3 x^{2} + 10 x - 1$ $y = −3x^2 + 10x − 1$ opens up or down and whether it has a maximum or minimum point?

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How do you determine whether the graph of $y = - 3 x^{2} + 10 x - 1$ $y = −3x^2 + 10x − 1$ opens up or down and whether it has a maximum or minimum point?

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Answer 1 · 2017-06-06T12:57:11

As the given equation has $- 3 x^{2}$ $-3x^2$ as the first term then the graph is of form $\cap$ $nn$ . That is, it opens down. Consequently the graph has a maximum point.

Explanation:

$Answering the question$ $color(blue)("Answering the question")$

If the coefficient of $x^{2}$ $x^2$ term is negative then the graph is of general form $\cap$ $nn$ and thus a maximum.

If the coefficient of the $x^{2}$ $x^2$ term is positive then the graph is of general form $\cup$ $uu$ and thus a minimum.

As the given equation has $- 3 x^{2}$ $-3x^2$ then the graph is of form $\cap$ $nn$ thus it has a maximum.
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Write the equation as $y = - 3 (x^{2} + (\frac{10}{- 3}) x) - 1$ $y=-3(x^2+(10/(-3))x) -1$

Then the $x$ $x$ value at the maximum is:

$(- \frac{1}{2}) \times (\frac{10}{- 3}) = + \frac{10}{6} = \frac{5}{3}$ $(-1/2)xx(10/(-3))=+10/6=5/3$

Tony B

Answer 2 · 2017-06-06T13:53:58

It depends on the sign of $a$ $a$ , the coefficient of the $x^{2}$ $x^2$ term.

Explanation:

Asking whether a parabola opens up or down, and whether it has a maximum or minimum point, is actually the same question:

It all depends on the sign of the $x^{2}$ $x^2$ term which we call $a$ $a$

$y = a x^{2} + b x + c$ $y =ax^2 +bx+c$

If $a$ $a$ is positive, ( $+ a x^{2}$ $" "+ax^2" "$ ) then the graph opens upwards, which also means that there is a minimum turning point.
(Smiling face parabola)

$a > 0 \to minimum TP$ $a > 0 rarr "minimum TP"$

If $a$ $a$ is negative, ( $- a x^{2}$ $" "-ax^2" "$ ) then the graph opens downwards, which also means that there is a maximum turning point.
(Sad face parabola)

$a < 0 \to maximum TP$ $a < 0 rarr "maximum TP"$

So, just look at the coefficient of $x^{2}$ $x^2$ and you will know immediately!

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How do you determine whether the graph of $y = - 3 x^{2} + 10 x - 1$ $y = −3x^2 + 10x − 1$ opens up or down and whether it has a maximum or minimum point?

2 Answers

Explanation:

Explanation:

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Science

Math

Humanities

... and beyond

How do you determine whether the graph of y = −3x^2 + 10x − 1y=−3x2+10x−1y = −3x^2 + 10x − 1 opens up or down and whether it has a maximum or minimum point?

2 Answers

Explanation:

Explanation:

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Impact of this question

How do you determine whether the graph of $y = - 3 x^{2} + 10 x - 1$ $y = −3x^2 + 10x − 1$ opens up or down and whether it has a maximum or minimum point?