Quadratic Axis of Symmetry

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. It can be found using the formula x = -b/(2a) from the quadratic equation ax² + bx + c.

Front

How do you find the vertex of a parabola given the equation in standard form?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k is the value of the function at h.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does the 'a' value in a quadratic equation determine?

Back

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

Front

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

Back

The 'b' value affects the position of the vertex along the x-axis and influences the axis of symmetry.

Front

What is the role of the 'c' value in a quadratic equation?

Back

The 'c' value represents the y-intercept of the parabola, which is the point where the graph crosses the y-axis.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression, look for two numbers that multiply to ac (the product of a and c) and add to b. Then, rewrite the expression using these numbers.

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 (b² - 4ac) tell us about the roots of a quadratic equation?

Back

The discriminant indicates the nature of the roots: if > 0, there are two real roots; if = 0, there is one real root; if < 0, there are no real roots.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' in the quadratic equation ax² + bx + c is positive, the parabola opens upwards; if negative, it opens downwards.