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2018-10-25T10:28:53+03:00
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https://peda.net/id/6812e906d83
2018-10-25T11:46:04+03:00
a) <img src="https://math-demo.abitti.fi/math.svg?latex=4x-3%3C0" alt="4x-3<0"/><br/>
<div>lasketaan nollakohdat</div>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=4x-3%3D0" alt="4x-3=0"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=4x%3D3" alt="4x=3"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B3%7D%7B4%7D" alt="x=\frac{3}{4}"/></div>
<div>merkkikaavio</div>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D%0A%26%26%5Cfrac%7B3%7D%7B4%7D%26%5C%5C%0A%5Chline%0A4x-3%26-%26%26%2B%0A%5Cend%7Barray%7D" alt="\begin{array}{l|l} &&\frac{3}{4}&\\ \hline 4x-3&-&&+ \end{array}"/></div>
<div>v: funktio saa negatiivisia arvoja kun x<3/4</div>
<div>b)
<div><img src="https://math-demo.abitti.fi/math.svg?latex=2x%5E2-5x%3C0" alt="2x^2-5x<0"/></div>
<div>lasketaan nollakohdat</div>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=2x%5E2-5x%3D0" alt="2x^2-5x=0"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%3D%5Cfrac%7B5%5Cpm%5Csqrt%7B%5Cleft(-5%5Cright)%5E2-4%5Ccdot2%5Ccdot0%7D%7D%7B4%7D" alt="x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{5\pm\sqrt{\left(-5\right)^2-4\cdot2\cdot0}}{4}"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B5%5Cpm5%7D%7B4%7D%3D2%5C%20%5Cfrac%7B1%7D%7B2%7D%5C%20tai%5C%200" alt="\frac{5\pm5}{4}=2\ \frac{1}{2}\ tai\ 0"/></div>
<div>lasketaan funktion arvoja testikohdissa</div>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(-1%5Cright)%3D2%5Cleft(-1%5Cright)%5E2-5%5Cleft(-1%5Cright)%3D2%2B5%3D7%3E0" alt="f\left(-1\right)=2\left(-1\right)^2-5\left(-1\right)=2+5=7>0"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(1%5Cright)%3D2%5Ccdot%5Cleft(1%5Cright)%5E2-5%5Cleft(1%5Cright)%3D2-5%3D-3%3C0" alt="f\left(1\right)=2\cdot\left(1\right)^2-5\left(1\right)=2-5=-3<0"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(3%5Cright)%3D2%5Ccdot3%5E2-5%5Cleft(3%5Cright)%3D18-15%3D3%3E0" alt="f\left(3\right)=2\cdot3^2-5\left(3\right)=18-15=3>0"/></div>
<div>merkkikaavio</div>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D%0A%26%260%26%262%5C%20%5Cfrac%7B1%7D%7B2%7D%26%5C%5C%0A%5Chline%0A2x%5E2-5x%26%2B%26%26-%26%26%2B%0A%5Cend%7Barray%7D" alt="\begin{array}{l|l} &&0&&2\ \frac{1}{2}&\\ \hline 2x^2-5x&+&&-&&+ \end{array}"/></div>
<div>v: funktio saa negatiivisia arvoja välillä 0<x<2 1/2</div>
<div>c) <br/>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=x%5E3%2B6x%5E2-7x%3C0" alt="x^3+6x^2-7x<0"/></div>
<div>lasketaan nollakohdat</div>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=x%5E3%2B6x%5E2-7x%3D0" alt="x^3+6x^2-7x=0"/></div>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cleft(x%5E2%2B6x-7%5Cright)%3D0" alt="x\left(x^2+6x-7\right)=0"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=x%3D0%5C%20tai%5C%20x%5E2%2B6x-7%3D0" alt="x=0\ tai\ x^2+6x-7=0"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%3D%5Cfrac%7B-6%5Cpm8%7D%7B2%7D%3D%5Cfrac%7B2%7D%7B2%7D%3D1%5C%20tai%5C%20-%5Cfrac%7B14%7D%7B2%7D%3D-7" alt="x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-6\pm8}{2}=\frac{2}{2}=1\ tai\ -\frac{14}{2}=-7"/></div>
<div>nollakohdat on x=-7, x=0 ja x=1</div>
<div>lasketaan funktion arvoja testikohdissa</div>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(-8%5Cright)%3D%5Cleft(-8%5Cright)%5E3%2B6%5Ccdot64-56%3D-568%2B384%3D-184%3C0" alt="f\left(-8\right)=\left(-8\right)^3+6\cdot64-56=-568+384=-184<0"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(-1%5Cright)%3D-1%2B6%2B7%3D12%3E0" alt="f\left(-1\right)=-1+6+7=12>0"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(0%7B%2C%7D5%5Cright)%5Capprox-1%7B%2C%7D88%3C0" alt="f\left(0{,}5\right)\approx-1{,}88<0"/><br/>
<img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(2%5Cright)%3D18%3E0" alt="f\left(2\right)=18>0"/></div>
<div>merkkikaavio</div>
<div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cbegin%7Barray%7D%7Bl%7Cl%7D%0A%26%26-7%26%260%26%261%26%5C%5C%0A%5Chline%0Ax%5E3%2B6x%5E2-7x%26-%26%26%2B%26%26-%26%26%2B%0A%5Cend%7Barray%7D" alt="\begin{array}{l|l} &&-7&&0&&1&\\ \hline x^3+6x^2-7x&-&&+&&-&&+ \end{array}"/></div>
<div>v:funktio saa negatiivisia arvoja kun -7<x tai 0<x<1</div>
</div>
</div>
2018-10-25T11:46:04+03:00