Intro to 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 graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula x = -b/(2a).

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

What is the significance of the positive zero in a quadratic function?

Back

The positive zero (or root) is the x-value where the function equals zero, indicating where the graph intersects the x-axis.

Front

How do you find the height of an object at its highest point in a quadratic application?

Back

The height at the highest point is found at the vertex of the parabola, specifically the y-coordinate of the vertex.

Front

What does the term 'application of quadratics' refer to?

Back

It refers to real-world problems that can be modeled using quadratic equations, such as projectile motion.

Front

How can you determine when an object reaches the ground using a quadratic equation?

Back

Set the height equation equal to zero and solve for t to find the time when the object is at ground level.

Front

What is the formula to find the vertex of a quadratic function in standard form?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h).

Front

What is the role of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward or downward) and affects the width of the graph.