How do you know if a parabola is vertical or horizontal?

If the x is squared, the parabola is vertical (opens up or down). If the y is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If it is negative, it opens down or to the left.

What is the axis of symmetry of a parabola?

The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric. To simplify, this line splits the graph of a quadratic equation into two mirror images.

How do you draw a solid vertical parabola?

Use the vertical parabola tool button on the graphing palette to draw a solid vertical parabola. Place the first point at the vertex of the parabola, shown as the solid dot on the graph, and place the second point at another location on the parabola, shown as the dashed curve on the graph.

What is vertical parabola?

If a parabola has a vertical axis, the standard form of the equation of the parabola is this: (x – h)2 = 4p(y – k), where p≠ 0. The vertex of this parabola is at (h, k). The focus is at (h, k + p). The directrix is the line y = k – p. The axis is the line x = h.

How do you find the axis of a parabola?

The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .

What is vertex parabola?

The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry. For a parabola whose equation is given in standard form , the vertex will be the minimum (lowest point) of the graph if and the maximum (highest point) of the graph if .

What is a vertical parabola?

The squaring of the variables in the equation of the parabola determines where it opens: When the x is squared and y is not, the axis of symmetry is vertical and the parabola opens up or down. For instance, y = x2 is a vertical parabola; its graph is shown.

How to find the coordinates of a parabola?

the coordinates another point P through which the parabola passes. Step 1: use the (known) coordinates of the vertex, (h, k), to write the parabola ‘s equation in the form: y = a(x − h)2 + k the problem now only consists of having to find the value of the coefficient a .

How to find the focal point of a parabola?

Measure the longest diameter (width) of the parabola at its rim.

Divide the diameter by two to determine the radius ( x) and square the result ( x2 ).

Measure the depth of the parabola ( a) at its vertex and multiply it by 4 (4 a ).

Divide the answer from Step 2 by the answer to Step 3 ( x2/4 a ).

What is the optimal value of a parabola?

The optimal value is the lowest or highest value in the parabola. The axis of symmetry is always written like y= optimal value. Find the optimal value of this vertex form equation y=2 (x+3)+9. The optimal value of this equation is y=9 because that is the k value in the equation.

What is the general equation for a parabola?

– a x ^ 2 + bx + c = 1 – a x ^ 2 + bx + c = 0 << quadratic equation – therefore standard parabolic form is y = a x ^ 2 + bx + c