Quadratics Review

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis. They can be found by setting the quadratic equation to zero and solving for x.

Front

If each mark on the x-axis represents one second, how do you determine when an object reaches the ground in a quadratic context?

Back

You find the x-value (time) at which the quadratic function equals zero, indicating the object has returned to the ground level.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on whether it opens upwards or downwards.

Front

How do you find the maximum value of a quadratic function?

Back

The maximum value occurs at the vertex of the parabola when it opens downwards. It is the y-coordinate of the vertex.

Front

What is the equation for 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. It can be found using the formula x = -b/(2a) from the standard form of the quadratic equation ax^2 + bx + c.

Front

What is the standard form of a quadratic equation?

Back

The standard form is written as y = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in a quadratic equation indicate about the graph?

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

How can you determine the number of real roots of a quadratic equation?

Back

You can determine the number of real roots by calculating the discriminant (b^2 - 4ac). If it's positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

What is the significance of the y-intercept in a quadratic function?

Back

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

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, identify the vertex, axis of symmetry, x-intercepts, and y-intercept, then plot these points and draw a smooth curve.