I want some formulas
Answers
Answer:
Let's solve the quadratic equation: x2 + 3x - 4 = 0
a = 1, b = 3, c = -4
\displaystyle x=\frac{-(3) \pm \sqrt{3^2 - 4 \cdot 1 \cdot (-4)}}{2 \cdot 1} =x=
2⋅1
−(3)±
3
2
−4⋅1⋅(−4)
=
\displaystyle = \frac{-3 \pm \sqrt{9 + 16}}{2} = \frac{-3 \pm \sqrt{25}}{2} ==
2
−3±
9+16
=
2
−3±
25
=
\displaystyle \frac{-3 \pm 5}{2} = \begin{cases} \frac{-3 - 5}{2} = -4 \\ \frac{-3 + 5}{2} = 1\end{cases}
2
−3±5
={
2
−3−5
=−4
2
−3+5
=1
Parabola
The graph of a quadratic equation is called a parabola.
If a > 0, then its vertex points down:
parabola with vertex down
If a < 0, then its vertex points up:
parabola with vertex up
If a = 0 the graph is not a parabola and a straight line.
The vertex of the parabola is at the point \displaystyle x = -\frac{b}{2a}x=−
2a
b
.
Vieta's formulas
If x1 and x2 are the roots of the quadratic equation ax2 + bx + c = 0 then:
\displaystyle x_1 + x_2 = -\frac{b}{a}x
1
+x
2
=−
a
b
\displaystyle x_1x_2 = \frac{c}{a}x
1
x
2
=
a
c
These formulas are called Vieta's formulas.
We can find the roots x1 and x2 of the quadratic equation by solving the simultaneous equations