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y = ax^2 + bx + c

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10y ago

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How do you write an equation for a parabola in standard form?

To write an equation for a parabola in standard form, use the format ( y = a(x - h)^2 + k ) for a vertical parabola or ( x = a(y - k)^2 + h ) for a horizontal parabola. Here, ((h, k)) represents the vertex of the parabola, and (a) determines the direction and width of the parabola. If (a > 0), the parabola opens upwards (or to the right), while (a < 0) indicates it opens downwards (or to the left). To find the specific values of (h), (k), and (a), you may need to use given points or the vertex of the parabola.


What is the standard equation of a parabola?

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


What is the standard equation of the parabola y3(x-4)2-22?

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


What is the standard form of the equation of a parabola that opens up or down?

The standard form of the equation of a parabola that opens up or down is given by ( y = a(x - h)^2 + k ), where ( (h, k) ) is the vertex of the parabola and ( a ) determines the direction and width of the parabola. If ( a > 0 ), the parabola opens upward, while if ( a < 0 ), it opens downward. The vertex form emphasizes the vertex's position and the effect of the coefficient ( a ) on the parabola's shape.


How do you rewrite the equation of a parabola in standard form?

To rewrite the equation of a parabola in standard form, you need to express it as ( y = a(x - h)^2 + k ) for a vertically oriented parabola or ( x = a(y - k)^2 + h ) for a horizontally oriented parabola. Here, ( (h, k) ) represents the vertex of the parabola, and ( a ) determines its direction and width. You can achieve this by completing the square on the quadratic expression.


How do you write 666 in standard form?

How do write 666 in standard form?


Can you write the equation of a parabola that doesn't cross the x-axis in factored form?

No.


How can you determine the orientation of a parabola when written in standard form?

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).


What is the standard form for a quadratic equation?

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


What does the point h k represent in x ay - k2 h the standard form of equation for a parabola?

In the standard form of the equation of a parabola, (y = a(x - h)^2 + k) or (x = a(y - k)^2 + h), the point ( (h, k) ) represents the vertex of the parabola. This point is crucial as it indicates the location where the parabola changes direction, and it serves as the minimum or maximum point depending on the orientation of the parabola. The value of (a) determines the width and the direction (upward or downward) of the parabola.


How do you write an equation of a parabola with vertex at the origin and the given focus 60?

To write the equation of a parabola with its vertex at the origin (0, 0) and a focus at (0, 60), you first identify the orientation of the parabola. Since the focus is above the vertex, the parabola opens upwards. The standard form of the equation for a parabola that opens upwards is ( y = \frac{1}{4p}x^2 ), where ( p ) is the distance from the vertex to the focus. Here, ( p = 60 ), so the equation becomes ( y = \frac{1}{240}x^2 ).


How do you write 2.35 in standard form?

It is already in standard form.