Question

Write the equation of a parabola that opens up or down in standard form and the equation of a parabola that opens left or right in standard form. Provide a sketch of the parabola for each one, label the vertex and axis of symmetry.

Short answer

The equation of a parabola that opens up or down in standard form is $y=a{(x-h)}^2+k$and that opens left or right in standard form is $x=a{(y-k)}^2+h$.

The sketches of each parabola is shown below:

Opens upwards:

Opens downwards:

Opens to the right:

Opens to the left:

Step-by-step solution

Step 1. Write the equation of a parabola that opens up or down in standard form and the equation of a parabola that opens left or right in standard form

The equation of a parabola that opens up or down in standard form is given by $y=a{(x-h)}^2+k$, where $(h,k)$is the vertex.

If localid="1645507694162" $a>0$, then the parabola opens upwards.

If $a<0$, then the parabola opens downwards.

The equation of a parabola that opens left or right in standard form is given by $x=a{(y-k)}^2+h$.

If $a>0$, then the parabola open to the right.

If $a<0$, then the parabola opens to the left.

Step 2. Draw a sketch of the parabola that opens upwards with the vertex and axis of symmetry.

Step 3. Draw a sketch of the parabola that opens downwards with the vertex and axis of symmetry.

Step 4. Draw a sketch of the parabola that opens to the right with the vertex and axis of symmetry.

Step 5. Draw a sketch of the parabola that opens to the left with the vertex and axis of symmetry.