Quadratics Graphs and their properties

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. It can be found using the formula x = -b/(2a) for a quadratic equation in the form ax^2 + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on whether it opens upwards or downwards.

Front

How do you find the roots or x-intercepts of a quadratic function?

Back

The roots or x-intercepts can be found by setting the quadratic equation equal to zero and solving for x, either by factoring, using the quadratic formula, or completing the square.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it means that the vertex is the minimum point of the graph, and the values of the function increase as you move away from the vertex.

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it means that the vertex is the maximum point of the graph, and the values of the function decrease as you move away from the vertex.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

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

Back

You can determine this by looking at the leading coefficient (a) of the quadratic function. If a > 0, it has a minimum; if a < 0, it has a maximum.

Front

What is the standard form of a quadratic equation?

Back

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

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: 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, find the vertex, axis of symmetry, y-intercept, and x-intercepts, then plot these points and draw a smooth curve through them.