Demonstrates graphically the relationship between the discriminant of the Quadratic Formula and the number of x-intercepts on the graph.

Nov 29, 2024 · What is a discriminant? The discriminant is the part of the quadratic formula that is under the square root sign It is sometimes denoted by the Greek letter (capital delta) How does the discriminant affect graphs and roots? There are three options for …

To calculate the discriminant of a quadratic equation, the formula is b2 – 4ac. Substitute the values of a, b and c after reading them from a quadratic equation of the form a𝑥2 + b𝑥 + c. For example, for 𝑥2 – 3𝑥 + 4, a = 1, b = -3 and c = 4. b2 = 9 and 4ac = …

Calculate the discriminant to determine the number and nature of the solutions of the following quadratic equation: y = x² − 2x + 1 y = x ² − 2 x + 1. Since the discriminant is zero, we should expect 1 real solution which you can see pictured in the graph below.

In this video, we find the number of roots, the type of roots, the equation of the parabola, and value of the discriminant from the graph of a quadratic func...

Let us explore how the discriminant affects the evaluation of \sqrt { { {b}^ {2}}-4ac} b2 −4ac in the quadratic formula and how it helps to determine the solution set. b^ {2}-4ac>0 b2 − 4ac> 0, then the number underneath the radical will be a positive value.

Apr 1, 2025 · Before we can find its discriminant, we must write the equation in standard form: a x 2 + b x + c = 0. Subtract 4 from each side of the equation: − 2 x 2 + x − 4 = 0. Find the discriminant: D = (1) 2 − 4 (− 2) (− 4) D = 1 − 32 = − 31. The value of the discriminant is negative; there are no real solutions to this quadratic equation.

To find the discriminant of a cubic equation or a quadratic equation, we just have to compare the given equation with its standard form and determine the coefficients first. Then we substitute the coefficients in the relevant formula to find the discriminant.

Nov 29, 2023 · This concept explores the discriminant and how to use the discriminant to describe the roots and graph of a quadratic function.

Dec 24, 2024 · STEP 1 - set the equations of the line and curve equal to each other. STEP 2 - rearrange to quadratic form. STEP 3 - find the discriminant and interpret its value. Since the discriminant is zero, the line and the curve intersect at one point only. Therefore the line is a tangent to the curve. Unlock more, it's free!