Quadratic Features

Front

What is the standard form of a quadratic equation?

Back

y = ax² + bx + c

Front

What does the axis of symmetry of a quadratic function represent?

Back

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

Front

What is the vertex of a quadratic function?

Back

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

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

If the coefficient 'a' in the standard form y = ax² + bx + c is positive, the parabola opens upwards and has a minimum. If 'a' is negative, it opens downwards and has a maximum.

Front

What is the significance of the 'a' value in the quadratic equation?

Back

The 'a' value determines the direction of the parabola (upward or downward) and affects the width of the parabola.

Front

What is the formula to find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a).

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by setting x = 0 in the equation.

Front

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

Back

The x-intercepts can be found by solving the equation ax² + bx + c = 0 using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What does the discriminant of a quadratic equation tell you?

Back

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