Solve Quadratic Equations by Graphing Review 2-21-25

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does the discriminant of a quadratic equation indicate about the number of x-intercepts?

Back

The discriminant (D = b² - 4ac) indicates the number of x-intercepts: D > 0 means 2 x-intercepts, D = 0 means 1 x-intercept, and D < 0 means 0 x-intercepts.

Front

Where is the axis of symmetry for a parabola given its vertex (h, k)?

Back

The axis of symmetry is the vertical line x = h, where (h, k) is the vertex of the parabola.

Front

What is the maximum number of solutions a quadratic equation can have?

Back

A quadratic equation can have a maximum of 2 solutions.

Front

If a quadratic equation has a discriminant of -3, how many x-intercepts does it have?

Back

It has 0 x-intercepts.

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.

Front

How do you find the vertex of a parabola from its standard form?

Back

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

Front

What is the effect of the coefficient 'a' in the quadratic equation y = ax² + bx + c?

Back

The coefficient 'a' determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Front

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

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating f(0) in the equation y = ax² + bx + c.

Front

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

Back

If 'a' is positive, the function has a minimum value at the vertex; if 'a' is negative, it has a maximum value.