Graphing Parabolas standard form

Front

What is the standard form of a parabola?

Back

The standard form of a parabola is given by the equation y = ax² + bx + c, where a, b, and c are constants.

Front

What does the coefficient 'a' in the parabola equation affect?

Back

The coefficient 'a' affects the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards. A larger absolute value of 'a' makes the parabola narrower.

Front

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

Back

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

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, dividing it into two mirror-image halves. Its equation is x = h, where h is the x-coordinate of the vertex.

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts (or roots) are the points where the parabola crosses the x-axis. They can be found by solving the equation ax² + bx + c = 0.

Front

What is the y-intercept of a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis. It can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form y = ax² + bx + c.

Front

How can you determine the direction of a parabola from its equation?

Back

You can determine the direction of a parabola by looking at the sign of the coefficient 'a'. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the significance of the vertex in a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction. It represents the maximum or minimum value of the quadratic function.

Front

How do you graph a parabola in standard form?

Back

To graph a parabola in standard form, identify the vertex, axis of symmetry, and intercepts. Plot these points and sketch the curve, ensuring it opens in the correct direction.

Front

What is the relationship between the vertex and the axis of symmetry?

Back

The vertex lies on the axis of symmetry, which is the line that divides the parabola into two symmetrical halves.