Question

Describe how to derive the quadratic formula from a quadratic equation in standard form

Answer 1

Firstly we learn the standard quadratic equation,

ax²+bx+c=0

where a,b,c are real numbers.

Now solve the quadratic equation using the Complete the square method.

Rewriting part of the equation as a perfect square trinomial. If you complete the square on the generic equation ax² + bx + c = 0 and then solve for x,

ax²+bx=-c

x² + $\frac{b}{a} x$=-c

add both the side $(\frac{b}{2a} )^{2}$

x² + $\frac{b}{a} x$+$(\frac{b}{2a})^{2} = -\frac{c}{a} + (\frac{b}{2a})^{2}$

$(x+\frac{b}{2a})^{2} = \frac{b^{2}-4ac}{4a^{2}}$`

take square root both the side

$x = \frac{-b+\sqrt{b^{2}-4ac}}{2a}$

$x= \frac{-b-\sqrt{b^{2}-4ac}}{2a}$

Answer 2

Answer:

The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square. The steps involve creating a perfect square trinomial, isolating the trinomial, and taking the square root of both sides. The variable is then isolated to give the solutions to the equation.

Step-by-step explanation:

:)