Solve the quadratic equation $$x^2 - 2x - 8 = 0$$ using the quadratic formula.

The solutions are $$x = 4$$ and $$x = -2$$ .

What is the significance of the leading coefficient in a quadratic equation?

The leading coefficient (a) determines the direction of the parabola: if a > 0, the parabola opens upwards; if a

Solve the quadratic equation $$2x^2 + 2x - 12 = 0$$ using the quadratic formula.

The solutions are $$x = 2$$ and $$x = -3$$ .

What is a quadratic equation?

A quadratic equation is a polynomial equation of degree 2, typically in the form $$ax^2 + bx + c = 0$$ where a, b, and c are constants and a ≠ 0.

What is the standard form of a quadratic function?

The standard form of a quadratic function is $$f(x) = ax^2 + bx + c$$ .

What is the vertex form of a quadratic function?

The vertex form of a quadratic function is $$f(x) = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

How can you find the y-intercept of a quadratic function?

The y-intercept can be found by evaluating the function at x = 0, which gives $$f(0) = c$$ .

What is the relationship between the roots and the coefficients of a quadratic equation?

The sum of the roots is given by $$-\frac{b}{a}$$ and the product of the roots is given by $$\frac{c}{a}$$ .

What is the role of the quadratic formula in solving quadratic equations?

The quadratic formula provides a systematic method to find the roots of any quadratic equation, regardless of whether the roots are real or complex.

Quadratic formula Flashcards

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