Quadratics in Context In Class Practice

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula (-b/2a, f(-b/2a)).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/2a.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph intersects the x-axis, found by solving the equation ax² + bx + c = 0.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0, which gives f(0) = c.

Front

How do you determine the number of solutions for a quadratic equation?

Back

The number of solutions can be determined using the discriminant (D = b² - 4ac). If D > 0, there are two solutions; D = 0 means one solution; D < 0 means no real solutions.

Front

What is the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height can be found at the vertex of the parabola, calculated using the formula f(-b/2a).

Front

How do you find the time a projectile is in the air?

Back

To find the time a projectile is in the air, determine the x-intercepts of the quadratic function, which represent the time when the projectile hits the ground.

Front

What is the significance of the coefficients a, b, and c in a quadratic function?

Back

The coefficient 'a' determines the direction and width of the parabola, 'b' affects the position of the vertex, and 'c' represents the y-intercept.