Vertex and axis of symmetry calculator

Parabola Calculator

vertex and axis of symmetry calculator

For a Quadratic Function find Vertex, Axis of Symmetry, Domain and Range, Intercepts

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This calculator finds x and y intercepts , vertex , focus and plots the quadratic function. The calculator will generate a detailed explanation for each of these computations. Coefficients can be either integers 10 , decimal numbers How to input?? So, in this case we will plot the graph using only two points. Welcome to MathPortal. I designed this web site and wrote all the lessons, formulas and calculators.

Your email address is safe with us. Read our Privacy Policy and Terms of Use. Sign up with Google. Give an overview of the instructional video, including vocabulary and any special materials needed for the instructional video. We recommend keeping it to paragraphs. Cancel Save. An updated version of this instructional video is available.

Index of lessons Print this page print-friendly version Find local tutors. For graphing, the leading coefficient " a " indicates how "fat" or how "skinny" the parabola will be. Also, if a is negative, then the parabola is upside-down. As you can see, as the leading coefficient goes from very negative to slightly negative to zero not really a quadratic to slightly positive to very positive, the parabola goes from skinny upside-down to fat upside-down to a straight line called a "degenerate" parabola to a fat right-side-up to a skinny right-side-up. There is a simple, if slightly "dumb", way to remember the difference between right-side-up parabolas and upside-down parabolas:. This can be useful information: If, for instance, you have an equation where a is negative, but you're somehow coming up with plot points that make it look like the quadratic is right-side-up, then you will know that you need to go back and check your work, because something is wrong.

Every parabola has an axis of symmetry which is the line that divides the graph into two perfect halves. On this page, we will practice drawing the axis on a graph , learning the formula , stating the equation of the axis of symmetry when we know the parabola's equation. Explore how the graph and equation relate to the axis of symmetry , by using our interactive program below. There are two different formulas that you can use to find the axis of symmetry. One formula works when the parabola's equation is in vertex form and the other works when the parabola's equation is in standard form.

The graph of a quadratic function is a parabola. The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola. The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. The vertex of the parabola is 2 , 1. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC.

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Practice: Features of quadratic functions: strategy. Finding features of quadratic functions. Practice: Features of quadratic functions. Practice: Graph parabolas in all forms. Comparing features of quadratic functions.

Quadratic function plotter

Find axis of symmetry and vertex

Minimum value is Use the vertex and the a-value to help outline what the parabola will look like. So the function you gave us is in vertex form. In this case, the minimum value is It is minimum because the parabola opens up. The axis of symmetry, is just the x-value of the vertex.


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