Quadratic Word Problems

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, 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 of the parabola (opening upwards or downwards).

Front

How do you find the maximum height of a projectile modeled by a quadratic equation?

Back

The maximum height can be found using the vertex formula t = -b/(2a) in the equation h(t) = at² + bt + c, where a and b are coefficients.

Front

What is the significance of the 'a' value in a quadratic equation?

Back

The 'a' value determines the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What does the discriminant of a quadratic equation tell us?

Back

The discriminant (b² - 4ac) indicates the number of real solutions: if positive, there are 2 solutions; if zero, there is 1 solution; if negative, there are no real solutions.

Front

How can you determine the time it takes for an object to hit the ground from a quadratic height equation?

Back

Set the height equation h(t) to zero and solve for t to find the time when the object reaches ground level.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you convert from standard form to vertex form?

Back

To convert, complete the square on the quadratic expression in 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 formula x = -b/(2a).