Quadratic Inequality Do Now 12/3

Front

What is a quadratic inequality?

Back

A quadratic inequality is an inequality that involves a quadratic expression, typically in the form ax² + bx + c < 0, ax² + bx + c > 0, etc.

Front

What does the graph of a quadratic inequality represent?

Back

The graph of a quadratic inequality represents the set of all points (x, y) that satisfy the inequality.

Front

How do you determine the direction of the inequality when graphing?

Back

The direction of the inequality (greater than or less than) determines whether the region above or below the parabola is shaded.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation (opening upwards or downwards).

Front

How do you find the zeros of a quadratic function?

Back

The zeros can be found by setting the quadratic equation to zero and solving for x, either by factoring, using the quadratic formula, or completing the square.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as y = a(x - r1)(x - r2), where r1 and r2 are the roots (zeros) of the equation.

Front

What does it mean if a parabola intersects the x-axis at two points?

Back

If a parabola intersects the x-axis at two points, it means the quadratic equation has two distinct real roots.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, no real roots.

Front

How do you graph a quadratic inequality?

Back

To graph a quadratic inequality, first graph the corresponding quadratic equation, then shade the appropriate region based on the inequality sign.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.