Quadratic Attributes

Front

What is the axis of symmetry for a parabola?

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 standard form of a quadratic equation ax^2 + bx + c.

Front

What is the vertex of a parabola in the form y = a(x - h)^2 + k?

Back

The vertex of the parabola is the point (h, k). It represents the highest or lowest point of the parabola depending on the value of 'a'.

Front

How do you determine if a parabola opens upwards or downwards?

Back

If the coefficient 'a' in the quadratic equation y = ax^2 + bx + c is positive, the parabola opens upwards. If 'a' is negative, the parabola opens downwards.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the formula to find the vertex of a parabola given in standard form?

Back

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

Front

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

Back

The 'a' value affects the width and direction of the parabola. A larger absolute value of 'a' makes the parabola narrower, while a smaller absolute value makes it wider.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the parabola crosses the y-axis, found by evaluating the function at x = 0, which gives the value c in the standard form y = ax^2 + bx + c.

Front

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

Back

The x-intercepts can be found by solving the equation ax^2 + bx + c = 0 using factoring, completing the square, or the quadratic formula x = (-b ± √(b² - 4ac)) / (2a).

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 is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula. It determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.