Turito Academy

Test Prep

Global form fields

As we can see from the graph we have a parabola curve and since it is opening in an upward direction. So we can say that a &gt; 0 and Hence, the option <span id="MathJax-Element-7-Frame" class="MathJax" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;">(a) is correct. Here, we can see that the vertex of the parabola is located in the fourth quadrant , therefore it will be = <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator b squared over denominator 2 a end fraction space greater than space 0" width="62" height="40" style="vertical-align:-13px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«mrow»«mn»2«/mn»«mi»a«/mi»«/mrow»«/mfrac»«mo»§#160;«/mo»«mo»§#62;«/mo»«mo»§#160;«/mo»«mn»0«/mn»«/math»'/> On further solving this, we get <img src="data:image/png;base64,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" class="Wirisformula" alt="b space less than space 0" width="45" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»b«/mi»«mo»§#160;«/mo»«mo»§#60;«/mo»«mo»§#160;«/mo»«mn»0«/mn»«/math»'/>  Therefore, the option <span id="MathJax-Element-10-Frame" class="MathJax" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;">(b) is also correct. Since, at <span id="MathJax-Element-11-Frame" class="MathJax" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;">x=0 , the y intercept will be positive and from this, we can conclude that <span id="MathJax-Element-13-Frame" class="MathJax" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;&amp;lt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;">c &lt; 0 and Hence, the option <span id="MathJax-Element-14-Frame" class="MathJax" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;">(c) will also be correct On checking all the options, and we can see all options are correct and Therefore, we conclude that all the options available are correct.

Graph of y = ax2 + bx + c = 0 is given adjacently. What conclusions can be drawn from this graph – <img src="data:image/png;base64,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" alt="" width="198" height="159" />

Solution for the question - graph of y = ax2 + bx + c = 0 is given adjacently. what conclusions can bedrawn from this graph c < 0