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- (c) When p > 0 and the axis of symmetry is the y-axis, the parabola opens up.
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Feb 14, 2022 · Since \(a=2\), the parabola opens upward. The axis of symmetry is \(x=h\). The axis of symmetry is \(x=1\). The vertex is \((h,k)\). The vertex is \((1,2)\). Find the \(y\)-intercept by substituting \(x=0\), \( \begin{align*} y &=3(x-1)^{2}+2 \\[4pt] y &=3 \cdot 0^{2}-6 \cdot 0+5 \\[4pt] y &=0 \end{align*} \) \(y\)-intercept \((0,5)\)
Nov 16, 2022 · So, this parabola will open up. Here are the vertex evaluations. \[\begin{align*}x = - \frac{4}{{2\left( 1 \right)}} = - \frac{4}{2} = - 2\\ & y = f\left( { - 2} \right) = {\left( { - 2} \right)^2} + 4\left( { - 2} \right) + 4 = 0\end{align*}\]
Jun 4, 2023 · The parabola is translated h units to the right if h > 0, and h units to the left if h < 0. The parabola is translated k units upward if k > 0, and k units downward if k < 0. The coordinates of the vertex are (h, k). The axis of symmetry is a vertical line through the vertex whose equation is x = h.
A parabola's axis of symmetry is perpendicular to the directrix. A parabola's axis of symmetry passes through its focus and vertex. The tangent at the vertex of a parabola is parallel to its directrix. A parabola's vertex is the midpoint of the focus and directrix through its axis of symmetry.
If you are using an equation for a parabola in the form of y=ax^2+bx+c then the sign of a ( the coefficient of the squared term ) will determine if it opens up or down. Sal has a video 'Introduction to parabola transformations' https://www.khanacademy.org/math/algebra/quadratics/transforming-quadratic-functions/v/shifting-and-scaling-parabolas ...
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- What would the equation be for a Parabola that is sideways?x=y^2 would create a parabola that goes sideways. Note: it would not be a function.
- does the parabolas ever "touch" and turn into an ellipse?I assume that you are talking about the lines of a parabola. If so, no. because then what you are looking at is not a parabola. It would be, as you...
- Why are they called "quadratics"?The Latin word for square is _quadratum_. Since the area of a square is the square of its side length, words similar to this are sometimes used to...
- can a parabola have a solution/root of zero?Yes - absolutely a parabola can have a root of zero. It just means the vertex or one of its x-intercepts is at (0,0).
- Is it possible to determine the magnitude of the curve of a parabola ? Like line graphs have slopes ...Yes, by comparing it to the parent function, y = x^2. On a graph, the parent function has the vertex at the origin (0,0) and additional reflexive p...
- Can a parabola be sideways?Yes. If a parabola is sideways, x is equal to y^2, instead of the other way around. Note that a sideways parabola isn't a function, though.
Feb 19, 2024 · (c) When p > 0 p > 0 and the axis of symmetry is the y-axis, the parabola opens up. (d) When p < 0 p < 0 and the axis of symmetry is the y -axis, the parabola opens down. The key features of a parabola are its vertex, axis of symmetry, focus, directrix, and latus rectum.
The distance between the vertex and the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola that is parallel to the directrix and passes through the focus. Parabolas can open up, down, left, right, or in some other arbitrary direction.
