OST Questions (pt 1)

Front

What are x-intercepts?

Back

The x-intercepts of a function are the points where the graph of the function crosses the x-axis. At these points, the value of the function is zero.

Front

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

Back

To find the x-intercepts of a quadratic function in the form f(x) = ax^2 + bx + c, set f(x) = 0 and solve for x using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is expressed as f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots (x-intercepts) of the function.

Front

What does it mean for a quadratic function to have a maximum or minimum vertex?

Back

A maximum vertex is the highest point on the graph of a quadratic function, while a minimum vertex is the lowest point. This depends on whether the parabola opens upwards (min) or downwards (max).

Front

How can you determine if a parabola opens up or down?

Back

The direction of a parabola is determined by the coefficient of the x² term in the quadratic equation. If the coefficient is positive, the parabola opens up; if negative, it opens down.

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

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

Back

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

Front

How do you match a graph with its equation?

Back

To match a graph with its equation, analyze key features such as the vertex, direction of opening, and intercepts, and compare them with the characteristics derived from the equation.

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 role of the leading coefficient in a quadratic function?

Back

The leading coefficient (a) affects the width and direction of the parabola. A larger absolute value of a makes the parabola narrower, while a smaller absolute value makes it wider.