Graphing Parabolas

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

Identify A, B, and C in the quadratic equation y=3x²-8+5x.

Back

A=3, B=5, C=-8.

Front

What is the axis of symmetry for the parabola represented by the equation y=x²-2x-3?

Back

The axis of symmetry is x = 1.

Front

Where does the axis of symmetry pass through in a parabola?

Back

The axis of symmetry passes through the vertex of the parabola.

Front

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

Back

The vertex is the point (h, k).

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 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 its width.

Front

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

Back

The discriminant (b² - 4ac) determines the number of real roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

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

Back

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

Front

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

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, then substitute back to find y.