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## General Form to Standard Form OR Vertex Form

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**General Form to Standard Form OR Vertex Form**By Completing the Square**+ Cx + Dy + E = 0**This term complicates things… we’ll leave it for Precal. All conic sections can be written in the general form Ax2 + Bxy + Cy2 + Dx + Ey+ F = 0. All conic sections can be written in the general form Ax2 + Bxy + Cy2 + Dx + Ey+ F = 0. How many squared terms? Are and both present? Do they have the same sign? Do they havethe samecoefficients? two yes yes Circle one no Parabola no Hyperbola Ellipse**Circle**Problem: Step 1 ---Rearrange the equation: ---x terms together on the left with a blank ---y terms together on the left with a blank ---constants on the right with 2 blanks Step 2 ---Fill in the blanks: ---half of the x term squared goes in the x blank and on the other side. ---half of the y term squared goes in the y blank and on the other side Step 3 ---factor the x trinomial ---factor the y trinomial ---Identify the conic**Ellipse**Problem: Step 1 ---Rearrange the equation: ---x terms together on the left with a blank ---y terms together on the left with a blank constants on the right with 2 blanks Step 2 ---Fill in the blanks: ---half of the x term squared goes in the x blank and on the other side. ---half of the y term squared goes in the y blank and on the other side ---multiply them by the numbers outside for the other blanks Step 3 ---factor the x trinomial ---factor the y trinomial ---Divide both sides by the constant on the right hand side. ---Identify the conic**Parabola**Problem: Step 1 ---non-squared variable is moved to the right along with the constant and a blank ---squared variable and corresponding terms on left with a blank Step 2 ---half the middle term squared goes in both blanks ---factor the squared trinomial ---factor out common value on the right Step 3 ---Move the factored out value to the other side by multiplying by the reciprocal. ---Identify the conic**Hyperbola**Problem: Step 1 ---Rearrange the equation: ---x terms together on the left with a blank ---y terms together on the left with a blank ---constants on the right with 2 blanks Step 2 ---Fill in the blanks: ---half of the x term squared goes in the x blank and on the other side. ---half of the y term squared goes in the y blank and on the other side ---multiply them by the numbers outside for the other blanks Step 3 ---factor the x trinomial ---factor the y trinomial ---Divide both sides by the constant on the right hand side. ---Identify the conic**On Your Own**a) b)**On Your Own**c) d) • x² + 8y + 4x - 4 = 0