Quadratic Applications

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the vertex of a parabola represent in a quadratic function?

Back

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction the parabola opens.

Front

How do you find the x-coordinate of the vertex of a quadratic function?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation ax² + bx + c.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of the quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

How can you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex, which can be found using the vertex formula and substituting the x-coordinate back into the function.

Front

What does it mean for a quadratic function to have a negative leading coefficient?

Back

If a quadratic function has a negative leading coefficient (a < 0), the parabola opens downward, indicating that the function has a maximum value.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as ax² + bx + c = 0, where a, b, and c are constants.

Front

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

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form.

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, given by the equation x = -b/(2a).

Front

How can you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form (px + q)(rx + s) = 0, then set each factor equal to zero and solve for x.