What Does It Mean When A Parabola Opens Up

One of the main points of a parabola is its vertex. Secondly the vertex of the parabola is the point left h k right. Learn why a parabola opens wider opens more narrow or rotates 180 degrees.

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Parabolas Open Up Or Down Min Or Max Youtube

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Parabolas Open Up Or Down Min Or Max Youtube

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What does it mean when a parabola opens up. First if a is positive then the parabola will open up and if a is negative then the parabola will open down. You can think of like an endpoint of a parabola. When will a quadratic function have a minimum or maximum. So i am gonna try to prove from slope perspective.

Home embed all precalculus resources. I hope it s clear that if our parabola opens upward then slope is positive else negative for say large positive x values. In this tutorial we will be looking at graphs of quadratic functions. First we know that this parabola is vertical opens either up or down because the x is squared.

For a vertical parabola h is inside parenthesis and since there is a negative in the pattern we must take the opposite. The children are transformations of the parent. There are two pieces of information about the parabola that we can instantly get from this function. It is the highest or the lowest point on its graph.

Some functions will shift upward or downward open wider or more narrow boldly rotate 180 degrees or a combination of the above. Vertical parabolas give an important piece of information. By yang kuang elleyne kase. The graph of a quadratic function is called a parabola and has a curved shape.

Create an account create tests flashcards. Remember a typical parabola can be written in the form y ax 2 bx c where a b and c are the coefficients in the quadratic function a is really useful in the quadratic function because it lets us know if the parabola opens up or down. Next we can find the vertex h k. Determine the direction in which a parabola opens study concepts example questions explanations for precalculus.

888 888 0446 precalculus. Be very careful with signs when getting the vertex. How can we determine if a parabola will open up or down. When you have a quadratic function in either form or if a 0 then the parabola opens up if a 0 then the parabola opens down the vertex is the lowest or highest point depending on direction on the graph of a quadratic function.

When the parabola opens up the vertex is the lowest point on the graph called the minimum or min when the parabola opens down the vertex is the highest point on the graph called the maximum or max. Call now to set up tutoring. We can determine it opens down because the a 2 is negative.