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How do you know if a quadratic equation is concave up or concave down?
That is simple. Think about linear equation and graphs. Think about rise over run. Vertical rise up is positive, rise down is negative. (by Stephen Hawking)
What is the equation of 7 to the negative 2 power as a positive?
7-2 IS positive. You do not need an equation for it. And if it were not positive, no correct equation would show it to be positive.
If the discriminant is positive are there real roots?
Yes. If the discriminant (of a quadratic equation) is...Positive: There are two real roots.Zero: There is a single "double" root. ("Double" means that if you factor, you will have a repeated factor.)Negative: There are two complex roots (and no real roots).
You are about to factor a quadratic equation involving some x's some x's and a plain numberyou see that the sign in front of te x's is negativeand the sign in front of the plain number is positive?
That means that both of your brackets will have minus signs.
How aerospace engineers use the quadratic equation?
The quadratic equation is used to find the intercepts of a function (F(x)=x^(2*n), n being an even number) along its primary axis (typically the x axis). Many equations follow this form. The information given by the quadratic equation depends on what your function is pertaining to. If say you have a velocity vs time graph, when the function crosses the xaxis your particle has changed from a positive velocity to a negative velocity. This information can be useful to determine the accompanying behavior of your position. The quadratic equation is simply a tool to find intercepts of a function.
