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- WE WANT TO GRAPH THE QUADRATIC FUNCTION H OF T = T/SQUARED + 5T + 4, USING THIS ONLINE GRAPHING TOOL. TO USE THIS TOOL WE FIRST HAVE TO SELECT THE PARABOLA GRAPHING TOOL HERE THEN CLICK ON THE VERTEX AND THEN ONE OTHER POINT ON THE PARABOLA. BUT BEFORE WE DO THIS LETS WORK OUT SOME THINGS BY HAND. THE FIRST THING WE SHOULD RECOGNIZE IS THAT THE GIVEN QUADRATIC FUNCTION IS IN GENERAL FORM OR THE FORM GIVEN HERE Y = AX/SQUARED + BX + C. WHEN WE HAVE A QUADRATIC FUNCTION THIS FORM HERE WE CAN FIND THE VERTEX USING THESE FORMULAS HERE WHERE THE X COORDINATE IS -B DIVIDED BY 2A. THIS ALSO GIVES US THE EQUATION TO THE AXIS OF SYMMETRY AND THEN THE Y COORDINATE IS F OF -B DIVIDED BY 2A. NOTICE HOW OUR QUADRATIC FUNCTION USES T INSTEAD OF X WHICH DOESNT MAKE A DIFFERENCE BUT IF ITS HELPFUL WE COULD WRITE THE GIVEN FUNCTION AS Y = X/SQUARED + 5X + 4. THIS WOULD PRODUCE THE SAME GRAPH. NOTICE A IS 1, B IS 5, AND C IS 4. SO IF WE WANT TO FIND THE COORDINATES OF THE VERTE