Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens up or down.

Front

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

Back

To find the x-intercepts, set y = 0 and solve the equation ax² + bx + c = 0.

Front

What is 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, given by the formula x = -b/(2a).

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola, depending on whether it opens down or up.

Front

How can you determine if a quadratic function has no real solutions?

Back

If the discriminant (b² - 4ac) is less than 0, the quadratic equation has no real solutions.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac that determines the nature of the roots of the quadratic equation.

Front

What does it mean if a quadratic function has two solutions?

Back

It means the graph of the function intersects the x-axis at two points.