Can a quadratic equation not equal to zeroWell I wanted to know whether or not y=x2+x+7 is a quadratic equation since the general form is ax2+bx+c=0 here the equation y=x2+x+7.

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Porter Camacho · Accepted Answer

When you write y=x2+x+7, that is not generally considered a &quot;quadratic equation&quot; in the commonly used sense. Most of the time, that is taken to mean a functional relationship between two variables, namely y and x. Because the right hand side takes the form of a quadratic polynomial, you are justified in calling it a &quot;quadratic function&quot; of x. When writing the relationship between two variables in this form, you&#039;re looking to answer questions like: what is the value of y for a given value of x? What does a plot of y against x look like? And so forth.A quadratic equation is (already, or can easily be rearranged into) something of the canonical form ax2+bx+c=0. The last term on the left hand side and is a constant term while the right hand side is zero.So these are quadratic equations:1. x2+x+7=0 (already in the canonical form)2. x2+x+7=2 (can be immediately rearranged into the canonical form)3. x2+x+7=k (where k is specified as a constant, even if it&#039;s not a known constant, allowing rearrangement into the proper form)Note that the quadratic functional relationship y=x2+x+7 can be made into a quadratic equation if we ask and try to answer questions like:1. What value(s) of x makes y=10? In this case x2+x+7=10, which is a quadratic equation with two real roots, so you have your two possible x values.2. Does the curve y=x2+x+7 intersect the x axis? The answer is &#039;no&#039; because the quadratic equation x2+x+7=0 has no real roots, only complex ones.

champe547 · Accepted Answer

It could be taken as both a relationship between y and x or as a quadratic equation, depending on the context of the problem.Most of the time the form y=ax2+bx+c is used to indicate the relationship between y and x. This is called is a quadratic function. But if it is given that y is a constant, then you could simply rewrite it as ax2+bx+(c−y)=0 and this is a quadratic equation.The difference between these two is that y in a quadratic function could have any value depending on the value of x. Whereas y in a quadratic equation is independent of x.

Can a quadratic equation not equal to zero Well

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