<p>GPS Algebra Converting from Standard to Vertex Form</p><p>The standard form of a quadratic equation is ax2 bx c 0 . The vertex form of a quadratic equation is a(x h)2 k 0 where (h, k) is your vertex. </p><p>Find the vertices of the following quadratic equations: 1. (x 5) 2 7 0 2. 2(x 4) 2 8 0 3. (x 6) 2 6 0</p><p>Once a quadratic equation is in vertex form it becomes easier to draw an accurate parabola. But how do you convert a quadratic equation from standard form to vertex form? Follow these steps:</p><p>STEP 1: Make sure that one side of the equation is equal to 0. STEP 2: Find the a value. The a value in vertex form is the same as the a value in standard form. STEP 3: Find the h value. In order to find the h value of a quadratic equation use the b formula , where a and b are the values from the standard form. 2a STEP 4: Find the k value. In order to find the k value of a quadratic equation, substitute your h value into your quadratic equation and solve. STEP 5: Place all of your values into the vertex form of a quadratic equation.</p><p>Ex 1: x 2 2x 4 STEP 1: Add 4 to both sides of the equation to make it x 2 2x 4 0 STEP 2: In the standard form, a = 1. Therefore, in vertex form a = 1 as well. b (2) 2 STEP 3: h = when b is -2, and a is 1. Therefore h = 1. 2a 2(1) 2 STEP 4: To find the value of k, substitute 1 into the equation x 2 2x 4 . (1) 2 2(1) 4 , 1 2 4 = 3. STEP 5: The vertex form of the standard quadratic equation x 2 2x 4 0 is (x 1) 2 3 0 .</p><p>Ex 2: 4x 2 16x 2 0 STEP 1: 4x 2 16x 2 0 STEP 2: a = 4 b 16 16 STEP 3: h = = = 2 2a 2(4) 8 STEP 4: 4(2)2 16(2) 2 = 4(4) 16(2) 2 = 16 32 2 = – 14 STEP 5: 4x 2 16x 2 0 is 4(x 2) 2 14 0 in vertex form.</p><p>Now you try a few: 1. x 2 2x 2 0 2. 2x 2 12x 25 0 3. x 2 12x 32 0</p><p>4. x 2 4x 7 0 5. x 2 6x 16 0 6. x 2 3x 3 0 Vertex to standard form</p><p>To change a quadratic equation from vertex to standard form we must simply follow order of operations. PEMDAS Step 1: Foil the squared binomial. Step 2: Distribute the “a” to the answer of your squared binomial. Step 3: Add the “k” to the other constant.</p><p>Change these equations from vertex to standard form. 7. y = 8(x + 1)2 – 7 8. Y = -(x + 3)2 + 6</p><p>9. y = -2(x – 1)2 – 4 10. Y = (x – 5)2 + 19</p>
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