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, meaning the y-coordinate is zero.

Front

How do 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.

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 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 has no real roots.

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, depending on the direction 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, passing through the vertex.

Front

What is the significance of the 'a' value in a quadratic equation?

Back

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

Front

What are the possible number of x-intercepts for a quadratic function?

Back

A quadratic function can have 0, 1, or 2 x-intercepts.

Front

What is the quadratic formula?

Back

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

Front

What does the discriminant (b² - 4ac) tell us about the x-intercepts?

Back

The discriminant indicates the number of x-intercepts: if > 0, there are 2; if = 0, there is 1; if < 0, there are none.