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What equation describes a parabola that opens up or down and whose vertex at the point (hv)?
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.
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?
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 right of the vertex.
How do you find the vertex of a parabola?
Solution 1Start by putting the parabola's equation into the form y = ax2 + bx + c if it opens up or down,or x = ay2 + by + c if it is opens to the left or right,where a, b, and c are constants.The x-value for the vertex is -(b/2a). You can use this x-value to solve for the y-value by substituting the x value in the original quadratic equation.Solution 2Put the parabola's equation into this form: y - k = 4p(x - h)2or x - h = 4p(y - k)2You just need to simplify the equation until it looks like this. The vertex is located at the coordinates (h,k). (p is for the focus, but that isn't important as long as you know h and k.)
How do you know if a parabola will open up or down by just looking at the equation?
when you write simple parabole eqn. y = x^2 it means when y = 9 x = -3 and x = +3 i.e x takes 2 values for one y. So graph has to open up. why "up" beacause eqn is for positive y.
What function is y equals axraised to the 2 power plus bx plus c?
This is the general form of a quadratic equation. The letters a, b, and c are constants to be supplied. a must be nonzero for it to remain a quadratic, but b and c can be any real numbers. It will plot a parabola, opening up or down, depending on the coefficient(a). Coefficient (a) will also determine how steeply the parabola changes. The coefficients b and c (along with a) will determine where the parabola is located.
