graphing quadratics

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.

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 vertex of a parabola?

Back

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

Front

How do you find the y-intercept of a quadratic equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

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 are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic crosses the x-axis, found by solving the equation ax² + bx + c = 0.

Front

What is the difference between maximum and minimum values in quadratics?

Back

A maximum value occurs at the vertex of a downward-opening parabola, while a minimum value occurs at the vertex of an upward-opening parabola.

Front

What is the factored form of a quadratic equation?

Back

The factored form is expressed as y = a(x - r1)(x - r2), where r1 and r2 are the roots or x-intercepts.

Front

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

Back

If the 'a' value in the quadratic equation is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: two real roots, one real root, or no real roots.