Can you have imaginary X intercepts?
If the solutions are imaginary, that means that the parabola has no x-intercepts (is strictly above or below the x-axis and never crosses it). If the solutions are real, but irrational (radicals) then we need to approximate their values and plot them.
How do you find the vertex of the quadratic function?
We find the vertex of a quadratic equation with the following steps:
- Get the equation in the form y = ax2 + bx + c.
- Calculate -b / 2a. This is the x-coordinate of the vertex.
- To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y.
How do you find imaginary roots?
Imaginary roots appear in a quadratic equation when the discriminant of the quadratic equation — the part under the square root sign (b2 – 4ac) — is negative. If this value is negative, you can’t actually take the square root, and the answers are not real.
What are the x-intercepts of a quadratic function?
x -intercepts of a Quadratic Function The x -intercepts of the function f (x) = a x 2 + b x + c, a ≠ 0 are the solutions of the quadratic equation a x 2 + b x + c = 0. The solutions of a quadratic equation of the form a x 2 + b x + c = 0 are given by the quadratic formula. x = − b ± b 2 − 4 a c 2 a
How to find the vertex of a quadratic function?
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 and write the function in vertex form. f (x) = ax 2 + bx + c.
Where are the x intercepts of the vertex?
The vertex is at (-1,4). The x intercepts, if any, are found by solving the equation f (x) = 0. Hence gives two solutions: x = 1 and x = – 3 ; hence x intercepts are at the points: (1 , 0) and (-3 , 0). Hence the y intercept is at the point (0 , 3). The axis of symmetry of the graph of the given quadratic function is a vertical line given by x = h.
How do you find the x intercept of an equation?
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.