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What best describes a single fixed point that is the same distance from the parabola as the directrix is from the parabola?
Locus
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.
What direction does the parabola open?
If the equation of the parabola isy = ax^2 + bx + c, then it opens above when a>0 and opens below when a<0. [If a = 0 then the equation describes a straight line, and not a parabola!].
What is the midpoint of the parabola between the focus and the directrix?
It is the apex of the parabola.
Does a parabola have to have an x-intercept?
No, a parabola does not have to have an x-intercept. ex. -2(x-2)^2 - 4 is a parabola that has no x-intercept.
What best describes a single fixed point that is the same distance from the parabola as the directrix is from the parabola?
Locus
The equation below describes a parabola. If a is negative which way does the parabola open y ax2?
Down
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.
What direction does the parabola open?
If the equation of the parabola isy = ax^2 + bx + c, then it opens above when a>0 and opens below when a<0. [If a = 0 then the equation describes a straight line, and not a parabola!].
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.
What is an equation that describes a parabola that opens left or right and whose vertex is at the point (h v)?
An equation that describes a parabola opening left or right with its vertex at the point ((h, v)) can be expressed as ((y - v)^2 = 4p(x - h)), where (p) determines the direction and width of the parabola. If (p > 0), the parabola opens to the right, and if (p < 0), it opens to the left.
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).
Can you solve X2 plus Y equals 63?
No you can't. There is no unique solution for 'x' and 'y'. The equation describes a parabola, and every point on the parabola satisfies the equation.
Which equation describes a parabola that opens up or down and whose vertex is at the point (hv)?
The equation that describes a parabola opening up or down with its vertex at the point ((h, v)) is given by (y = a(x - h)^2 + v), where (a) is a non-zero constant. If (a > 0), the parabola opens upwards, while if (a < 0), it opens downwards. The vertex form allows easy identification of the vertex and the direction of the parabola's opening.
The equation below describes a parabola. If a is positive which way does the parabola open?
If the coefficient ( a ) in the equation of a parabola (typically given in the form ( y = ax^2 + bx + c )) is positive, the parabola opens upwards. This means that the vertex of the parabola is the lowest point, and as you move away from the vertex in either direction along the x-axis, the y-values increase.
What The equation y ax2 describes a parabola. If the value of a is positive which way does the parabola open?
If the value of ( a ) in the equation ( y = ax^2 ) is positive, the parabola opens upwards. This means that the vertex of the parabola is the lowest point, and as you move away from the vertex in either direction along the x-axis, the value of ( y ) increases. Conversely, if ( a ) were negative, the parabola would open downwards.
Which equation describes a parabola that opens left or right and whose vertex is at the point (hv)?
The equation that describes a parabola opening left or right with its vertex at the point ((h, k)) is given by ((y - k)^2 = 4p(x - h)), where (p) determines the direction and width of the parabola. If (p > 0), the parabola opens to the right, while if (p < 0), it opens to the left. Here, ((h, k)) represents the vertex coordinates.
