Graphing Quadratics Review

Front

What is the vertex of the quadratic function y = (x-4)² + 3?

Back

The vertex is (4, 3).

Front

What is the axis of symmetry for the quadratic function y = (x-4)² + 3?

Back

The axis of symmetry is x = 4.

Front

How do you find the vertex of a quadratic function in standard form y = ax² + bx + c?

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)).

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax² + bx + c.

Front

What are the roots of a quadratic function?

Back

The roots are the values of x where the function intersects the x-axis, also known as x-intercepts.

Front

What is the formula to find the x-coordinate of the vertex of a quadratic function?

Back

The formula is x = -b/(2a).

Front

What do the coefficients a, b, and c represent in the standard form of a quadratic function?

Back

a is the coefficient of x², b is the coefficient of x, and c is the constant term.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

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

Front

What is the relationship between the vertex and the axis of symmetry in a quadratic function?

Back

The axis of symmetry passes through the vertex and divides the parabola into two mirror-image halves.

Front

How can you determine the number of real roots a quadratic function has?

Back

You can determine the number of real roots by calculating the discriminant (b² - 4ac). If it's positive, there are two real roots; if zero, one real root; if negative, no real roots.