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What is maximum or minimum of a parabola depending on whether the parabola opens up or down?
Vertex
To find the value of a in a parabola opening up or down, subtract the y-value of the parabola at the vertex from the y-value of the point on the parabola that is one unit to the of the vertex?
right
What is the standard equation for vertex at origin opens down 1 and 76 units between the vertex and focus?
Since the vertex is at the origin and the parabola opens downward, the equation of the parabola is x2 = 4py, where p < 0, and the axis of symmetry is the y-axis. So the focus is at y-axis at (0, p) and the directrix equation is y = -p. Now, what do you mean with 1 and 76 units? 1.76 units? If the distance of the vertex and the focus is 1.76 units, then p = -1.76, thus 4p = -7.04, then the equation of the parabola is x2 = -7.04y.
Is it true graph is reflected about the x-axis and the parabola opens down?
No. A parabola can open up or down.
What does calculate the vertex mean in math terms?
Most likely you have an equation of a parabola. The vertex of a parabola is the location where it changes from going down, to going up (a simplified explanation). Most parabolas that we think of are oriented up or down (the axis is parallel to the y axis), but they could be oriented sideways, or even at an angle. To calculate the vertex of a parabola ususally means to find the coordinates of the vertex.
