SOLUTION: Look at the graph above and comment on the sign of the discriminant. Form the quadratic equation based on the information provided and find its solutions. * This graph is a Pa

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Look at the graph above and comment on the sign of the discriminant. Form the quadratic equation based on the information provided and find its solutions. * This graph is a Pa      Log On


   

Question 330684: Look at the graph above and comment on the sign of the discriminant. Form the quadratic equation based on the information provided and find its solutions.
* This graph is a Parabola type. You can tell by its horse shoe shape and in a upright position
* The x2 coefficient term is positive, because of the upward opening. This tells me the formula ax^2 + bx + c = >0 is used. In addition, two real roots exist for a positive.
* Because the graph crosses the x axis, one or more real roots exist.
* A visible symmetrical (lowest point) exist and is called the vertex. This position is on coordinates (-0.16,-2). Additionally, the vertex is located between a mirror image of the left and right lines.

Answer by solver91311(24713) About Me  (Show Source):
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Since there are two intercepts, there are two distinct real number roots, hence the discriminant is positive.

However, there is insufficient information to determine the specific quadratic function or its zeros.

Using the coordinates of the vertex, you can determine two vital pieces of information. First since the -coordinate of the vertex of the general quadratic function is given by , you can use the fact that the -coordinate of the vertex is to write a linear equation relating and



and you can also write another linear equation relating , , and by using the vertex coordinates since we know that any point on the function can be described as :





and by substitution:




But that is as far as we can go without additional information. The only thing that can be said for certain about the zeros of the function is that there exists a real number such that the -intercepts of the graph of your function are at:



and




The coordinates of any other point on the graph of your function would be sufficient to uniquely determine the coefficients.

John

My calculator said it, I believe it, that settles it