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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.
How do you find y and x intercept of parabola?
For the equation of any graph. The graph intercepts the y-axis, when x is zero, so in the equation, substitute x=0, and solve for y. To find the x-intercept, this is when y is zero, so substitute y=0, and solve for x. For a parabola, if the highest power of y is the 1st power (no exponent) and the highest power of x is 2, then the parabola opens up or down. The parabola will have 1 y-intercept (usually it is the constant value), and depending on where it is (if it is at the origin, it is also an x-intercept, and the other x-intercept has the same distance as y-intercept has from the axis of symmetry i.e y = a2x + bx), either have 2 x-intercepts, or no interceptions with the x-axis (i.e. y = x2 + c, c ≥ 0 or y = -x2 + c, c ≤ 0). If the highest power of y is 2, and highest power of x is 1, then it opens left or right, and it may have none or 2 y-intercepts, and will have 1 x-intercept. So when you're solving for the one that's a quadratic, if you come up with imaginary or complex roots, that means there is no intercept.
Determine whether the parabola y equals -x2 plus 15x plus 8 opens up down left or right?
when you have y=+/-x2 +whatever, the parabola opens up y=-(x2 +whatever), the parabola opens down x=+/-y2 +whatever, the parabola opens right x=-(y2 +whatever), the parabola opens left so, your answer is up
The maximum or minimum of a parabola depending on whether the parabola opens up or down?
A parabola opening up has a minimum, while a parabola opening down has a maximum.
Is it true graph is reflected about the x-axis and the parabola opens down?
No. A parabola can open up or down.
What is maximum or minimum of a parabola depending on whether the parabola opens up or down?
Vertex
How do you tell if a parabola opens up or down?
To determine if a parabola opens up or down, look at the coefficient of the quadratic term in its equation, typically in the form (y = ax^2 + bx + c). If the coefficient (a) is positive, the parabola opens upwards; if (a) is negative, it opens downwards. You can also visualize the vertex: if the vertex is the lowest point, it opens up, and if it's the highest point, it opens down.
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 find a parabola opening up or down?
If you can mash the equation for the parabola into the form Y = Ax2 + Bx + C, then the parabola opens up if 'A' is positive, and down if 'A' is negative.
Which equation describes a parabola that opens up or down and whose vertex is at the point (h v)?
The equation that describes a parabola that opens up or down with its vertex at the point (h, v) is given by the vertex form of a quadratic equation: ( y = a(x - h)^2 + v ), where ( a ) determines the direction and width of the parabola. If ( a > 0 ), the parabola opens upwards, while if ( a < 0 ), it opens downwards.
The equation y -3x2 describes a parabola. Which way does the parabola open?
The given terms can't be an equation without an equality sign but a negative parabola opens down wards whereas a positive parabola opens up wards.
Given the standard equation for a parabola opening up or down which way does a parabola open when the coefficient of the x2 term a is positiveUp or down?
In that case it opens upwards.
When does a parabola open down?
No, a parabola is the whole curve, not just a part of it.
What equation describes a parabola that opens up or down and whose vertex is at the point (h v)?
The equation that describes a parabola opening up or down with its vertex at the point ((h, v)) is given by the standard form (y = a(x - h)^2 + v), where (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 ((h, v)) is the minimum or maximum point of the parabola, depending on the sign of (a).
