Q: Given the standard equation for a parabola opening left or right which way does a parabola open when the coefficient of the y2-term a is positive?

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If the coefficient of x2 is positive then the parabola is cup shaped (happy face). If the coefficient of x2 is negative then the parabola is cap shaped (gloomy face).

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In that case it opens upwards.

There is no such thing as a standard equation. Furthermore, there are standard forms - all different - for the equation of a line, a circle, a plane, a parabola, an ellipse and so on. the question needs to be more specific.

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If the coefficient of x2 is positive then the parabola is cup shaped (happy face). If the coefficient of x2 is negative then the parabola is cap shaped (gloomy face).

down

In that case it opens upwards.

the standard form of the equation of a parabola is x=y2+10y+22

There are two standard form of parabola: y2 = 4ax & x2 = 4ay, where a is a real number.

This is called the 'standard form' for the equation of a parabola:y =a (x-h)2+vDepending on whether the constant a is positive or negative, the parabola will open up or down.

The standard equation for a Parabola with is vertex at the origin (0,0) is, x2 = 4cy if the parabola opens vertically upwards/downwards, or y2 = 4cx when the parabola opens sideways. As the focus is at (0,6) then the focus is vertically above the vertex and we have an upward opening parabola. Note that c is the distance from the vertex to the focus and in this case has a value of 6 (a positive number). The equation is thus, x2 = 4*6y = 24y

There is no such thing as a standard equation. Furthermore, there are standard forms - all different - for the equation of a line, a circle, a plane, a parabola, an ellipse and so on. the question needs to be more specific.

Normally a quadratic equation will graph out into a parabola. The standard form is f(x)=a(x-h)2+k

focus , directrix

x= ay² + by + c Apex :3