Key Features of Quadratic Graphs

Front

What is a quadratic graph?

Back

A quadratic graph is a graph of a quadratic function, which is a polynomial function of degree 2, typically in the form y = ax² + bx + c.

Tags

CCSS.HSF-IF.C.7A

Front

What does the vertex of a quadratic graph represent?

Back

The vertex of a quadratic graph represents the highest or lowest point of the graph, depending on the direction it opens (upward or downward).

Front

What is the significance of the y-intercept in a quadratic graph?

Back

The y-intercept is the point where the graph crosses the y-axis, representing the value of the function when x = 0.

Tags

CCSS.HSF-IF.C.7A

Front

How do you find the x-intercepts of a quadratic graph?

Back

The x-intercepts can be found by setting the quadratic equation to zero and solving for x, which gives the points where the graph crosses the x-axis.

Tags

CCSS.HSF-IF.C.7A

Front

What is the axis of symmetry in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the graph into two mirror-image halves, passing through the vertex.

Front

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

Back

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

Tags

CCSS.HSF-IF.C.7A

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 is the vertex form of a quadratic equation?

Back

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

Front

How can you determine if a quadratic graph opens upward or downward?

Back

If the coefficient 'a' is positive, the graph opens upward; if 'a' is negative, the graph opens downward.

Tags

CCSS.HSF-IF.C.7A

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex, depending on whether the parabola opens downward (maximum) or upward (minimum).