Graphing Quadratics Homework

Front

What is a parabola?

Back

A parabola is a symmetrical, curved shape that represents the graph of a quadratic function. It can open upwards or downwards.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the axis of symmetry for a parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the quadratic equation ax^2 + bx + c.

Front

What does the axis of symmetry represent?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c.

Front

How do you determine if a parabola opens upwards or downwards?

Back

If the coefficient 'a' in the quadratic function is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

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

Back

The 'a' value determines the width and direction of the parabola. A larger absolute value of 'a' makes the parabola narrower.

Front

How can you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form.

Front

What are the roots or solutions of a quadratic equation?

Back

The roots are the x-values where the parabola intersects the x-axis, found by solving the equation f(x) = 0.

Front

What is the quadratic formula?

Back

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