Front

What is a quadratic inequality?

Back

A quadratic inequality is an inequality that involves a quadratic expression, typically in the form ax^2 + bx + c < 0, ax^2 + bx + c > 0, ax^2 + bx + c ≤ 0, or ax^2 + bx + c ≥ 0.

Front

How do you determine the direction of a parabola given a quadratic equation?

Back

The direction of a parabola is determined by the coefficient of the x^2 term. If the coefficient is positive, the parabola opens upwards; if it is negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a parabola, and why is it important?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens up or down. It is important because it represents the maximum or minimum value of the quadratic function.

Front

How can you find the maximum height of a projectile modeled by a quadratic function?

Back

To find the maximum height, you can use the vertex formula x = -b/(2a) to find the time at which the maximum height occurs, then substitute that time back into the function to find the height.

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of the quadratic equation. If it is positive, there are two distinct real roots; if it is zero, there is one real root; if it is negative, there are no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve a quadratic inequality graphically?

Back

To solve a quadratic inequality graphically, you first graph the corresponding quadratic equation, identify the x-intercepts, and then determine the intervals where the quadratic expression is above or below the x-axis.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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 find the time when a projectile reaches a certain height?

Back

To find the time when a projectile reaches a certain height, set the height equation equal to the desired height and solve for the variable representing time.

Front

What is the formula for the height of an object in free fall?

Back

The height of an object in free fall can be modeled by the equation h(t) = -16t^2 + vt + h0, where v is the initial velocity and h0 is the initial height.