QUadratics: Standard form

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the vertex of a parabola represent?

Back

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

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting x back into the equation to find y.

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 evaluating the function at x = 0.

Front

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

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 axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What does it mean if a parabola has a maximum value?

Back

A parabola has a maximum value if it opens downwards (a < 0), indicating the vertex is the highest point.

Front

What does it mean if a parabola has a minimum value?

Back

A parabola has a minimum value if it opens upwards (a > 0), indicating the vertex is the lowest point.

Front

How can you determine the number of real roots of a quadratic equation?

Back

The number of real roots can be determined using the discriminant (D = b² - 4ac): D > 0 means 2 real roots, D = 0 means 1 real root, D < 0 means no real roots.

Front

What is the formula for the quadratic formula?

Back

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