how to make a quadratic equation in vertex form Finding the vertex of the quadratic by using the equation x b 2a and then substituting that answer for y in the orginal equation Then substitute the vertex into the vertex form equation y a x h 2 k a will stay the same h is x and k is y
Let us consider a quadratic equation in Vertex Form color blue y f x x 3 2 8 where color green a 1 h 3 k 8 Hence color blue Vertex 3 8 To find the y intercept set color red x 0 y 0 3 2 8 y 9 8 Step 1 To convert a general standard form of a quadratic equation a x 2 b x c 0 to the vertex form a x h 2 k 0 find h the x coordinate of the
how to make a quadratic equation in vertex form
how to make a quadratic equation in vertex form
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Write Quadratic Equation In Vertex Form Slideshare
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Convert Quadratic Equation To Standard Form Example 1 YouTube
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Use the technique of completing the square to place the given quadratic function in vertex form Set up a coordinate system on a sheet of graph paper Label and scale each axis Draw the axis of symmetry and label it with its equation Plot the vertex and label it with its coordinates Y a x h 2 k is the vertex form equation Now expand the square and simplify You should get y a x 2 2hx h 2 k Multiply by the coefficient of a and get y ax 2 2ahx ah 2 k This is standard form of a quadratic equation with the normal a b and c in ax 2 bx c equaling a 2ah and ah 2 k respectively
While the standard quadratic form is ax 2 bx c y the vertex form of a quadratic equation is bi y bi a bi x bi h 2 bi k In both forms y is the y coordinate x is the x coordinate and a is the constant that tells you whether the parabola is facing up a or down a Y 2 x 5 2 4 This equation is in vertex form y a x h 2 k This form reveals the vertex h k which in our case is 5 4 It also reveals whether the parabola opens up or down Since a 2 the parabola opens downward This is enough to start sketching the graph A coordinate plane
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Step 1 Isolating the x 2 and x terms to one side of the equation y x 2 12x 32 y 32 x 2 12x Step 2 Add b 2 2 to both sides of the equation Here b 12 2 2 36 Thus y 32 36 x 2 12x 36 y 4 x 2 12x 36 Step 3 Factor the right side of the equation into a perfect square y 4 x 6 2 The standard form of a quadratic equation is ax 2 bx c The vertex form of a quadratic equation is a x h 2 k where a is a constant that tells us whether the parabola opens upwards or downwards and h k is the location of the vertex of the parabola
Just as a quadratic equation can map a parabola the parabola s points can help write a corresponding quadratic equation Parabolas have two equation forms standard and vertex In the vertex form y a x h 2 k y a x h 2 k the variables h and k are the coordinates of the parabola s vertex In the standard form 96 11K views 11 years ago Standard to Vertex Form by Completing the Square Learn how to write a quadratic equation from standard form to vertex form by completing the square A
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how to make a quadratic equation in vertex form - Y 2 x 5 2 4 This equation is in vertex form y a x h 2 k This form reveals the vertex h k which in our case is 5 4 It also reveals whether the parabola opens up or down Since a 2 the parabola opens downward This is enough to start sketching the graph A coordinate plane