SOLUTION: Determine whether the graph of each parabola opens upward or downward. y= -1/2^x^2+3 Please help me to understand what parabola means. Textbook Elementary and Intermedia

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Determine whether the graph of each parabola opens upward or downward. y= -1/2^x^2+3 Please help me to understand what parabola means. Textbook Elementary and Intermedia      Log On


   



Question 32006: Determine whether the graph of each parabola opens upward or downward.
y= -1/2^x^2+3
Please help me to understand what parabola means.

Textbook Elementary and Intermediate Algebra. Mark Dugopolski
ISBN: 13978-0-07-326862-0

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
A parabola is one of the "conic sections", so-called beacause it's one of the curves you get when you slice a right-circular cone in one of several ways.
The other conic sections are:
The circle, the ellipse, and the hyperbola.
You can "see" the parabola when you graph a quadratic equation.
You can tell which way the parabola opens from the sign of the coefficient of the x%5E2-term.
If this coefficient is positive, the parabola opens upward.
If this coefficient is negative, the parabola opens downward.
In your problem, the quadratic equation is:
y+=+%28-1%2F2%29x%5E2+%2B+3 and you can see that the coefficient of the x%5E2-term -1%2F2 is negative, so the parabola opens downward.
Here's the graph of your equation:
graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C-%281%2F2%29x%5E2%2B3%29