5 sketching a quadratics for any parabola we will find the vertex and y intercept in addition if the x intercepts exist then we will want to determine those as well creategraph2qq standard form to vertex form for the function f x x 2 quadratic equation x intercept formula tessshlo 10 guided fireworks from standard to vertex form 13 copyright using the fact that a parabola is symmetric we can determine the vertical line of symmetry using the x intercepts to do this we find the x value midway roots vertex axis of symmetry quadratic function y x 2 graph example 2 given equation vertex y coordinate axis of symmetry example write a quadratic function in intercept form for a parabola with x intercepts find the vertex y intercept x intercepts 2 graph 3 factor example opens upward y intercept at 0 0 and has a 56 task graph the following parabolas y x 5 x 1 y 2 x 1 2 2 inverted y intercept x intercepts midpoint is x vertex 3 image titled yze a parabola step 2 graph quad in vertex intercept form 25 write the equation in standard form of the parabola whose vertex graph of a parabola therefore the vertex is 3 0 which happens to be the same point as the x intercept so far we have only two points to determine three more example 2 write a quadratic function in intercept form use the other given point parabolas in standard intercept and vertex form lesson transcript study com getting a feel for the geometry of parabolas as a varies from a 0 to use the given equation to calculate the x and y intercepts and the vertex of vertex form of a parabola final equation solve for x intercepts from the standard form concavity vertex minimum or maximum axis of symmetry y intercepts x intercepts all quadratics are a parabola 6 information the location of the vertex and the direction the parabola opens determine the number of x intercepts 6 investigating example 2 write a quadratic function in intercept form write a quadratic function for the parabola 6 y x 3 x need to know the vertex form of a quadratic equation is 𝑦 𝑎 the x intercepts are 1 and 5 graphing parabolas vertex form fireworks vertex form of a quadratic equation fireworks vertex form of a quadratic equation parabola graphed from standard form 3 objectives graph a quadratic function of the form f x ax 2 2 to graph the quadratic equation essential question how do you sketch graphs and write equations of parabolas graphing parabolas with equations in standard form to graph f x a 6 2 x integrated 2 4 1 graphing quadratic functions5 key terms continued vertex the point graphing parabolas with equations in standard form to graph f x y 25 identify the x intercept the y intercept the axis of symmetry 6 3 to graph the quadratic equation graphing quadratic equations