Question

Deriving Equations of Quadratic functions Help

x= -½ x=7


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Answer 1

Answer:When we are asked to solve a quadratic equation, we are really being asked to find the roots. We have already seen that completing the square is a useful method to solve quadratic equations. This method can be used to derive the quadratic formula, which is used to solve quadratic equations. In fact, the roots of the function,

f (x) = ax2 + bx + c

are given by the quadratic formula. The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation,

ax2 + bx + c = 0.

We can do this by completing the square as,

quadratic equation derovation part Ix= -½ x=7

Solving for x and simplifying we have,

quadratic equation derivation part 2

Thus, the roots of a quadratic function are given by,

x =( -b + or - (square root (b^2 -4ac))/2a

This formula is called the quadratic formula, and its derivation is included so that you

otice that the discriminant of f(x) is greater than zero,

b2− 4ac = (−11)2− 4 · 2 · 5 = 121 − 40 = 81.

This function is graphically represented by a parabola that opens upward whose vertex lies below the x-axis. Thus, the graph must intersect the x-axis in two places (i.e. has two roots)

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