Section 1.5 – Solve Quadratic Equations - McGraw-Hill Ryerson

) The parabola opens upward and the vertex islocated above the x-axis, so the function has nozeros.The equation 8x 2 11x 5 5 0 has no realsolutions.c) The parabola opens downward and the vertexis located on the x-axis. This function has onezero.The equation 4x 2 12x 9 5 0 has onesolution.The graph of a quadratic function gives you a visual understanding ofthe number of x-intercepts. Without a graphing calculator, it can bequite time-consuming to create this visualization. Is there a way that thenumber of zeros can be identified without drawing a graph? The nextexample revisits Example 2 using the quadratic formula to see if a patterncan be identified that will tell the number of zeros without graphing.Example 3ConnectionsEngineers use the zerosof a quadratic functionto help mathematicallymodel the supportstructure needed for abridge that must span agiven distance.Connect the Number of Zeros to the Quadratic FormulaSolve each quadratic equation in Example 2 using the quadratic formula.Give answers for the x-intercepts as exact values. Compare the resultswith the conclusion for the number of x-intercepts found in Example 2.Solutiona) 2x 2 8x 5 5 0a 5 2, b 5 8, and c 5 5.________x 5 ​ b ____ ​ b 2 4ac ​2a_______________5 ​ 8 _____ ​ 8 2 4(2)(5) ​​2(2)___5 ​___8 ​ 24 ​4 ____x 5 ​___8 2​ 6 ​​or x 5 ​___8 2​ 6 ​44____x 5 ​__4 ​ 6 ​ or x 5 ​__4 ​ 6 ​22The answer of two solutions from Example 2 is verified by thequadratic formula. There are two solutions because the valueunder the radical sign is positive, so it can be evaluated to give twoapproximate roots.46 MHR • Functions 11 • Chapter 1