Exploring Quadratic Functions

What is a quadratic function?

• A quadratic function is a linear function of degree one.

• A quadratic function is a polynomial function of degree three.

• A quadratic function is a polynomial function of degree two, expressed as f(x) = ax^2 + bx + c.

• A quadratic function is expressed as f(x) = ax + b.

Which of the following is a quadratic equation?

• ax + b = 0

• ax^2 + bx + c = 0

• x^2 - 4 = 0 + d

• x^3 + 2x + 1 = 0

How can you identify a quadratic function from its equation?

• The equation must include an x^2 term with a non-zero coefficient.

• The equation must be in the form of y = mx + b.

• The equation can include a constant term only.

• The equation must have only linear terms.

What is the standard form of a quadratic function?

• f(x) = ax^2 + bx + c

• f(x) = a + b + c

• f(x) = ax^3 + bx + c

• f(x) = ax^2 + b

What is the vertex of a parabola?

• The vertex is the point where the parabola intersects the x-axis.

• The vertex of a parabola is the point (h, k) where it changes direction.

• The vertex is always located at the origin (0,0).

• The vertex is the highest point of the parabola only.

How do you find the vertex of a quadratic function?

• The vertex is located at the midpoint of the x-intercepts.

• The vertex is always at (0, 0).

• The vertex is at (x, y) where x = -b/(2a) and y is the function value at that x.

• The vertex can be found by using the quadratic formula directly.

What does the direction of a parabola indicate?

• The direction of a parabola indicates whether it opens upwards or downwards.

• The direction of a parabola shows its color.

• The direction of a parabola indicates its width.

• The direction of a parabola reveals its vertex position.

If a parabola opens upwards, what can you say about its leading coefficient?

• The leading coefficient is zero.

• The leading coefficient is negative.

• The leading coefficient can be any real number.

• The leading coefficient is positive.

How do you determine the x-intercepts of a quadratic function?

• Set the quadratic function to zero and solve for x.

• Identify the coefficients and write the function in vertex form.

• Use the quadratic formula to find the y-intercepts.

• Graph the function and find the vertex.

What is the formula to find the roots of a quadratic equation?

• x = (b ± √(4ac - b²)) / (2c)

• x = (-b ± √(b² - 4ac)) / (2a)

• x = (b ± √(b² + 4ac)) / (2a)

• x = (-b ± 2√(b² - 4ac)) / a