Graphing Quadratic Equations

Front

What is the axis of symmetry in a quadratic equation?

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 y = ax^2 + bx + c.

Front

How do you find the vertex of a quadratic equation?

Back

The vertex of a quadratic equation in the form y = ax^2 + bx + c can be found using the formula: Vertex (h, k) where h = -b/(2a) and k = f(h).

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

Back

The 'a' value determines the direction of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the significance of the 'c' value in a quadratic equation?

Back

The 'c' value represents the y-intercept of the quadratic function, which is the point where the graph intersects the y-axis.

Front

How do you graph a quadratic equation?

Back

To graph a quadratic equation, find the vertex, axis of symmetry, and y-intercept. Then plot additional points on either side of the vertex to create the parabolic shape.

Front

What is the formula to find the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the discriminant in a quadratic equation?

Back

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

Front

What is the vertex of the equation y = x^2 - 4x + 3?

Back

The vertex can be found using h = -b/(2a). Here, h = 2, and substituting back gives k = -1. So, the vertex is (2, -1).

Front

How do you determine if a quadratic function has a maximum or minimum value?

Back

If 'a' is positive, the function has a minimum value at the vertex. If 'a' is negative, it has a maximum value at the vertex.