Properties of a Graph of Quadratic Equation

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic equation look like?

Back

The graph of a quadratic equation 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 downwards or upwards.

Front

How do you find the axis of symmetry of 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 significance of the y-intercept in a quadratic graph?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.

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What is the significance of the x-intercepts in a quadratic graph?

Back

The x-intercepts are the points where the graph crosses the x-axis, found by solving the equation y = 0.

Front

What does it mean if a quadratic function has no real roots?

Back

If a quadratic function has no real roots, it means the graph does not intersect the x-axis, indicating that the discriminant (b² - 4ac) is less than zero.

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 the parabola opens upwards?

Back

If the parabola opens upwards, the coefficient 'a' in the quadratic equation is positive, indicating a minimum value at the vertex.

Front

What does it mean if the parabola opens downwards?

Back

If the parabola opens downwards, the coefficient 'a' in the quadratic equation is negative, indicating a maximum value at the vertex.