Once you calculate the X coordinate using the axis of symmetry (X=-b/2a), you plug that value in for all of the X's in the equation of the parabola. You then solve the equation for the value of Y.
Since the vertex is at the origin and the parabola opens downward, the equation of the parabola is x2 = 4py, where p < 0, and the axis of symmetry is the y-axis. So the focus is at y-axis at (0, p) and the directrix equation is y = -p. Now, what do you mean with 1 and 76 units? 1.76 units? If the distance of the vertex and the focus is 1.76 units, then p = -1.76, thus 4p = -7.04, then the equation of the parabola is x2 = -7.04y.
For example, y = ax2 + bx + c (the equation of a parabola). Every parabola has an axis of symmetry and the graph to either side of the axis of symmetry is a mirror image of the other side. It means that if we know a point on one side of the parabola, we can find its symmetric point to the other side, based on the axis of symmetry. Those symmetric points have opposite x-coordinate values, and the same y-coordinate value. The vertex only is a single point which lies on the axis of symmetry.
y=x2-12x+7
These are called the zeros of the equation. They are the places where y=0
Did you mean a parabola with equation y=3x^2? The line of symmetry is x=0 or the y-axis.
Line of symmetry: x = 3
How about y = (x - 2)2 = x2 - 4x + 4 ? That is the equation of a parabola whose axis of symmetry is the vertical line, x = 2. Its vertex is located at the point (2, 0).
Once you calculate the X coordinate using the axis of symmetry (X=-b/2a), you plug that value in for all of the X's in the equation of the parabola. You then solve the equation for the value of Y.
The line of symmetry located on a parabola is right down the center. A parabola is a U shape. Depending on the direction of the parabola it either has a x axis of symmetry or y axis of symmetry. You should have two equal sides of the parabola.
The axis of symmetry is x = -2.
Parallel to the y-axis, going through the highest/lowest point of the parabola (if the parabola is negative/positive, respectively).
Set y = 0 and solve for x, with a parabola you should get one, two, or no x-axis crossings, it depends on the equation and the location on the x-y axis of the parabola.
Since the vertex is at the origin and the parabola opens downward, the equation of the parabola is x2 = 4py, where p < 0, and the axis of symmetry is the y-axis. So the focus is at y-axis at (0, p) and the directrix equation is y = -p. Now, what do you mean with 1 and 76 units? 1.76 units? If the distance of the vertex and the focus is 1.76 units, then p = -1.76, thus 4p = -7.04, then the equation of the parabola is x2 = -7.04y.
Yes. think of a parabola that curves around the y-axis. an equation like x = square root of (y2 - 9) simply switch the x's and y's in the equation and your parabola opens up around the y-axis and the x-axis respectively
For example, y = ax2 + bx + c (the equation of a parabola). Every parabola has an axis of symmetry and the graph to either side of the axis of symmetry is a mirror image of the other side. It means that if we know a point on one side of the parabola, we can find its symmetric point to the other side, based on the axis of symmetry. Those symmetric points have opposite x-coordinate values, and the same y-coordinate value. The vertex only is a single point which lies on the axis of symmetry.
Your equation must be in y=ax^2+bx+c form Then the equation is x= -b/2a That is how you find the axis of symmetry