X-Intercepts of Quadratics-Graphs

Front

What are x-intercepts in a quadratic graph?

Back

X-intercepts are the points where the graph of a quadratic function crosses the x-axis. At these points, the value of y is zero.

Front

How can you find the x-intercepts of a quadratic equation?

Back

To find the x-intercepts, set the quadratic equation equal to zero and solve for x. This can be done using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions (x-intercepts) of the quadratic equation ax² + bx + c = 0.

Front

What does it mean if a quadratic graph has no x-intercepts?

Back

If a quadratic graph has no x-intercepts, it means the graph does not cross the x-axis, indicating that the quadratic equation has no real solutions.

Front

What is the significance of the vertex in relation to x-intercepts?

Back

The vertex of a quadratic graph is the highest or lowest point on the graph. The position of the vertex relative to the x-axis can indicate whether the graph has x-intercepts.

Front

If a quadratic equation has two x-intercepts, what does this indicate about its graph?

Back

If a quadratic equation has two x-intercepts, the graph is a parabola that opens either upwards or downwards and crosses the x-axis at two distinct points.

Front

What does it mean if a quadratic equation has one x-intercept?

Back

If a quadratic equation has one x-intercept, the graph touches the x-axis at a single point, known as a double root, indicating that the vertex lies on the x-axis.

Front

What is the relationship between the discriminant and the number of x-intercepts?

Back

The discriminant (b² - 4ac) determines the number of x-intercepts: if it's positive, there are two x-intercepts; if zero, one x-intercept; if negative, no x-intercepts.

Front

How do you determine the x-intercepts from a graph?

Back

To determine the x-intercepts from a graph, look for the points where the graph intersects the x-axis. These points are the x-intercepts.

Front

What are the coordinates of the x-intercepts for the equation y = x² - 4?

Back

The x-intercepts are (2,0) and (-2,0), found by setting y = 0 and solving the equation x² - 4 = 0.