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9.5 Ease of Setup DocHub User Ratings on G2 9.0 Ease of Use DocHub User Ratings on G2 The easiest way to edit worksheet graphing quadratics from standard form answer key in PDF format online Handling paperwork with our comprehensive and user-friendly PDF editor is easy. Adhere to the instructions below to fill out worksheet graphing quadratics from standard form answer key online quickly and easily:Log in to your account. Sign up with your credentials or register a free account to try the product before upgrading the subscription.Upload a form. Drag and drop the file from your device or import it from other services, like Google Drive, OneDrive, Dropbox, or an external link.Edit worksheet graphing quadratics from standard form answer key. Quickly add and highlight text, insert images, checkmarks, and signs, drop new fillable areas, and rearrange or remove pages from your document.Get the worksheet graphing quadratics from standard form answer key completed. Download your modified document, export it to the cloud, print it from the editor, or share it with other participants through a Shareable link or as an email attachment.Make the most of DocHub, one of the most easy-to-use editors to rapidly handle your documentation online!be ready to get more Complete this form in 5 minutes or lessGet form be ready to get more Complete this form in 5 minutes or lessGet form A quadratic equation is a polynomial equation of degree 2 . The standard form of a quadratic equation is 0 = a x 2 + b x + c where a , b and c are all real numbers and a ≠ 0 . If we replace 0 with y , then we get a quadratic function y = a x 2 + b x + c whose graph will be a parabola . The axis of symmetry of this parabola will be the line x = − b 2 a . The axis of symmetry passes through the vertex, and therefore the x -coordinate of the vertex is − b 2 a . Substitute x = − b 2 a in the equation to find the y -coordinate of the vertex. Substitute few more x -values in the equation to get the corresponding y -values and plot the points. Join them and extend the parabola. Example 1: Graph the parabola y = x 2 − 7 x + 2 . Compare the equation with y = a x 2 + b x + c to find the values of a , b , and c . Here, a = 1 , b = − 7 and c = 2 . Use the values of the coefficients to write the equation of axis of symmetry . The graph of a quadratic equation in the form y = a x 2 + b x + c has as its axis of symmetry the line x = − b 2 a . So, the equation of the axis of symmetry of the given parabola is x = − ( − 7 ) 2 ( 1 ) or x = 7 2 . Substitute x = 7 2 in the equation to find the y -coordinate of the vertex. y = ( 7 2 ) 2 − 7 ( 7 2 ) + 2 = 49 4 − 49 2 + 2 = 49 − 98 + 8 4 = − 41 4 Therefore, the coordinates of the vertex are ( 7 2 , − 41 4 ) . Now, substitute a few more x -values in the equation to get the corresponding y -values.
Plot the points and join them to get the parabola.
Example 2: Graph the parabola y = − 2 x 2 + 5 x − 1 . Compare the equation with y = a x 2 + b x + c to find the values of a , b , and c . Here, a = − 2 , b = 5 and c = − 1 . Use the values of the coefficients to write the equation of axis of symmetry. The graph of a quadratic equation in the form y = a x 2 + b x + c has as its axis of symmetry the line x = − b 2 a . So, the equation of the axis of symmetry of the given parabola is x = − ( 5 ) 2 ( − 2 ) or x = 5 4 . Substitute x = 5 4 in the equation to find the y -coordinate of the vertex. y = − 2 ( 5 4 ) 2 + 5 ( 5 4 ) − 1 = − 50 16 + 25 4 − 1 = − 50 + 100 − 16 16 = 34 16 = 17 8 Therefore, the coordinates of the vertex are ( 5 4 , 17 8 ) . Now, substitute a few more x -values in the equation to get the corresponding y -values.
Plot the points and join them to get the parabola.
Example 3: Graph the parabola x = y 2 + 4 y + 2 . Here, x is a function of y . The parabola opens "sideways" and the axis of symmetry of the parabola is horizontal. The standard form of equation of a horizontal parabola is x = a y 2 + b y + c where a , b , and c are all real numbers and a ≠ 0 and the equation of the axis of symmetry is y = − b 2 a . Compare the equation with x = a y 2 + b y + c to find the values of a , b , and c . Here, a = 1 , b = 4 and c = 2 . Use the values of the coefficients to write the equation of axis of symmetry. The graph of a quadratic equation in the form x = a y 2 + b y + c has as its axis of symmetry the line y = − b 2 a . So, the equation of the axis of symmetry of the given parabola is y = − 4 2 ( 1 ) or y = − 2 . Substitute y = − 2 in the equation to find the x -coordinate of the vertex. x = ( − 2 ) 2 + 4 ( − 2 ) + 2 = 4 − 8 + 2 = − 2 Therefore, the coordinates of the vertex are ( − 2 , − 2 ) . Now, substitute a few more y -values in the equation to get the corresponding x -values.
Plot the points and join them to get the parabola.
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