Graphing Quadratics(Key Features)

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) for a quadratic equation in the form ax^2 + bx + c.

Front

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

Back

To find the y-intercept, substitute x = 0 into the quadratic equation and solve for y.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis. They can be found by setting the quadratic equation equal to zero and solving for x.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

Front

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

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is written as f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

You can determine the direction by looking at the 'a' value in the quadratic equation. If 'a' > 0, it opens upwards; if 'a' < 0, it opens downwards.

Front

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

Back

The discriminant (D = b^2 - 4ac) determines the nature of the roots of the quadratic equation. If D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, identify the vertex, axis of symmetry, y-intercept, and x-intercepts. Plot these points and draw a smooth curve through them.

Front

What is the formula for the vertex of a parabola 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 function at x = h.