Find Vertex and Intercepts of Quadratic Functions - Calculator
An easy to use calculator to find the vertex, x and y intercepts of the graph of a quadratic function of the form.
f(x) = ax2 + bx + c
Vertex of the graph of a Parabola
The vertex of the graph of a parabola is the maximum or minimum point of the graph. This online calculator uses the formulas
h = - b / 2a
k = f(h)
to find the x and y coordinates h and k,respectively, of the vertex of a parabola.
x and y intercepts of the graph of a Parabola
To find the x intercepts, the calculator solves the quadratic equation ax2 + bx + c = 0 using the quadratic formulas:
x1 = (- b + √Δ) / (2 a)
x2 = (- b - √Δ) / (2 a)
where Δ = b2 - 4 a c is the discriminant.
The y intercept if given by f(0) = c.
How to use the calculator
1 - Enter the coefficients a, b, c and the number of decimal places as real number and press "enter". The x coordinates of the x intercepts are displayed. If the two coordinates are equal, the graph touches the x axis and the two x intercepts have equal x coordinates. The x intercepts may not exist. The y coordinate of the y intercept is also displayed. The x and y coordinates of the vertex are also displayed at the bottom.