Quadratics in Standard Form

Front

What is a quadratic equation in standard form?

Back

A quadratic equation in standard form is expressed as ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

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 'a' in the equation.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation.

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph crosses the x-axis, found by solving the equation ax² + bx + c = 0.

Front

What is the y-intercept of 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 many zeros can a quadratic function have?

Back

A quadratic function can have 0, 1, or 2 zeros, depending on the discriminant (b² - 4ac).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac that determines the number of real solutions (zeros) of the quadratic equation.

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real solutions.