Equations

Quadratic Equation: Graph and Formula

The discriminant, the formula and the roots as the x-intercepts of a parabola

  • High school
  • about 5 min
  • 1 of 3 in the family
Not started
2x2+3x−7=02x^2 + 3x - 7 = 0
-2.771.27

The dashed yellow line is the axis x = −b/2a. The roots lie symmetrically around it, √D / 2|a| away.

a = 2
b = 3
c = -7
D=b2−4ac=32−4⋅2⋅(−7)=65D = b^2 - 4ac = 3^2 - 4 \cdot 2 \cdot (-7) = 65
x1,2=−b±D2a=−3±654x_{1,2} = \frac{-b \pm \sqrt{D}}{2a} = \frac{-3 \pm \sqrt{65}}{4}
x1=−3−654,x2=−3+654x_1 = \frac{-3 - \sqrt{65}}{4},\quad x_2 = \frac{-3 + \sqrt{65}}{4}

D > 0: the parabola crosses the x-axis twice - two solutions.

Where it is taught