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, ax² + bx + c ≤ 0, or ax² + bx + c ≥ 0.

Front

What does it mean for a parabola to have zeros?

Back

Zeros of a parabola are the x-values where the graph intersects the x-axis, meaning the output (y-value) is zero.

Front

How do you find the zeros of a quadratic function?

Back

To find the zeros of a quadratic function, you can set the function equal to zero and solve for x using factoring, completing the square, or the quadratic formula.

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 is the vertex of a parabola?

Back

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

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, passing through the vertex.

Front

How can you determine if a quadratic opens upwards or downwards?

Back

A quadratic opens upwards if the leading coefficient (a) is positive and downwards if it is negative.

Front

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

Back

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

Front

What does it mean for a quadratic inequality to be 'greater than' or 'less than'?

Back

'Greater than' means the values of the quadratic expression are above the x-axis, while 'less than' means they are below the x-axis.

Front

How do you graph a quadratic inequality?

Back

To graph a quadratic inequality, first graph the corresponding quadratic equation as a boundary, then shade the region that satisfies the inequality.