Graph Quadratic Equations in Standard Form

Front

What is the standard form of a quadratic equation?

Back

y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the 'a' in the quadratic equation represent?

Back

The 'a' value determines the direction and width of the parabola. If a > 0, the parabola opens upwards; if a < 0, it opens downwards.

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, given by the formula x = -b/(2a).

Front

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

Back

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

Front

What are the roots of a quadratic equation?

Back

The roots (or zeros) are the x-values where the graph intersects the x-axis, found by solving the equation y = 0.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What does the 'b' in the quadratic equation represent?

Back

The 'b' value affects the position of the vertex along the x-axis and the steepness of the parabola.

Front

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

Back

The 'c' value represents the y-intercept of the parabola, where the graph crosses the y-axis.

Front

How can you determine if a quadratic equation has real roots?

Back

By calculating the discriminant (D = b² - 4ac). If D > 0, there are two real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, characterized by its U-shape.