Quadratic Formula and Discriminant

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the discriminant (D) represent in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the number and type of solutions of a quadratic equation. If D > 0, there are two real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Front

If the discriminant is negative, what can we conclude about the solutions of the quadratic equation?

Back

If the discriminant is negative, the quadratic equation has no real solutions.

Front

What does it mean if a quadratic graph does not intersect the x-axis?

Back

If a quadratic graph does not intersect the x-axis, it indicates that the equation has no real solutions.

Front

How do you identify the coefficients a, b, and c in a quadratic equation?

Back

In the quadratic equation ax² + bx + c = 0, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Front

Given the quadratic equation 4x² - 8x = 3, what are the values of a, b, and c?

Back

For the equation 4x² - 8x - 3 = 0, the values are a = 4, b = -8, c = -3.

Front

What is the significance of the value of the discriminant in determining the nature of the roots?

Back

The value of the discriminant indicates whether the roots are real or complex, and whether they are distinct or repeated.

Front

Calculate the discriminant for the equation 6x² - 2x - 3 = 0.

Back

For the equation 6x² - 2x - 3 = 0, the discriminant is D = (-2)² - 4(6)(-3) = 4 + 72 = 76, indicating two real solutions.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a).

Front

What type of solutions does a quadratic equation have if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real solution, also known as a repeated or double root.