![]() ![]() ![]() y-intercept reflection (6,10) x = 1 and x = 5 7. y-intercept reflection (- 4,1) x = and x = 7. y-intercept reflection (-8,7) x = -1 and x = -7 7. By doing so we have a parabola that is in vertex form.Presentation on theme: "Using the Vertex Form of Quadratic Equations"- Presentation transcript:ġ Using the Vertex Form of Quadratic Equationsģ Example 1 Given an equation: y = (x + 4)2 – 9 Determine: Looking carefully at the expression in the parenthesis we can see that it is a perfect square which we can factor. When doing this you must remember the Golden Rule: "Do unto one side of an equation as you would do unto the other." However this time are are going to keep one side the SAME x 2 + 8x - 20 = y ( x 2 + 8x + 16) - 20 -16 = yīy adding AND subtracting 16 from both sides we are in effect keeping the left side of the equation the same and now have: Vertex form of a quadratic equation: A quadratic equation in the form of a(xh)2+k 0 a ( x h) 2 + k 0, where a, h, and k are constants and ( h, k) is the vertex. » Lesson Plan and Student Assessment documents are also available. Therefore, in order to convert an equation to Vertex Form we must use the methods discussed in the last unit.Īs before, when completing the square you must first make one side of the equation a perfect square. Quadratic Functions in Vertex Form is the last of four activities for teaching and learning quadratic equations in algebra: Graphing Quadratic Equations Quadratic Word Problems Part 1 Quadratic Word Problems Part 2 and Quadratic Functions in Vertex Form. The inverse of FOILing is factoring through various methods, particularly through completing the square. Think of converting from Standard Form as the inverse of converting form Vertex Form. In the previous section we learned that converting from Vertex Form is a matter of FOILing or multiplying binomials. Media:Solutions to Converting from Vertex Form to Standard Form.pdf Converting Standard Form to Vertex FormĬonverting from Standard Form to Vertex form is a little more difficult than converting from Vertex Form to Standard Form. Try convert the following equations in vertex form to standard form and click the link to check your answers. Remembering that squaring a binomial is the same as multiplying by itself we can rewrite this equation as:Ĭombining like terms we find that our equation originally written in vertex form is now in standard form: Let us look at an equation in vertex form. Recalling basic algebra we can easily transform the equation. If you are presented with a parabola whose given form makes it difficult to answer a given question algebraically you should try to convert the given equation into the other form.Ĭonverting between vertex form to standard form is a matter of FOILing. Vertex Form is give in the form ( x - h) 2 + k = y To help aid in the understanding of the different constants a, h, and k take a look at the following TI-Nspire document.īoth forms of parabolas have certain advantages and disadvantages. Let us turn to a different form of parabolas: Vertex Form. We use Standard Form because it is very useful to find the zeros as seen in our previous lesson. However, using another method can be extremely helpful when translating a parabola. Translating a parabola up and down is extremely difficult to do. The center of the parabola called the axis of symmetry is affected by both the a and b as seen in the diagram to the left. The b value does not control how far a parabola "moves" left and right. (This a value is the same a value discusses in the next section for Vertex Form) ![]() The a value controls how quickly the parabola rises or drops.The c value is the initial height of the parabola. ![]() Let us look at Parabolas in Standard Form: If a parabola is given in another form it must be converted to Standard Form. The quadratic formula only can be used to find the zeros of a parabola in Standard Form. The examples given in the previous lesson were all given in Standard Form. Standard Form of a Parabola can be very useful for analyzing parabolas. ![]()
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