Quadratic Graphs

Front

What is the vertex of a quadratic graph?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, represented as a coordinate (h, k) in the vertex form y = a(x - h)² + k.

Front

What are the X-intercepts of a quadratic graph?

Back

The X-intercepts are the points where the graph crosses the X-axis, found by setting the quadratic equation to zero and solving for x.

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

What are the coordinates of the Y-intercept in a quadratic graph?

Back

The Y-intercept is the point where the graph crosses the Y-axis, represented as (0, c) in the standard form y = ax² + bx + c.

Front

What is the shape of the graph of a quadratic function called?

Back

The graph of a quadratic function is called a parabola.

Front

What does the coefficient 'a' in the quadratic equation y = ax² + bx + c determine?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

What is the axis of symmetry in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

How do you find the vertex from the standard form of a quadratic equation?

Back

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

Front

What is the quadratic formula used for?

Back

The quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), is used to find the roots (solutions) of a quadratic equation.

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, which determines the nature of the roots.