Quadratic applications

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, represented as (h, k) in the vertex form of a quadratic equation y = a(x - h)² + k.

Front

How do you find the x-coordinate of the vertex in a quadratic equation?

Back

Use the formula x = -b/(2a) where a and b are coefficients from the standard form of the quadratic equation ax² + bx + c.

Front

What does it mean when a quadratic equation is set to zero?

Back

Setting a quadratic equation to zero allows you to find the x-intercepts (roots) of the function, which are the points where the graph intersects the x-axis.

Front

What is the significance of the maximum height in a projectile motion problem?

Back

The maximum height represents the peak point of the projectile's trajectory, which can be found at the vertex of the quadratic function modeling the height.

Front

How do you determine when an object hits the ground in a quadratic application?

Back

Set the height equation equal to zero and solve for the time variable.

Front

What is the formula for the height of a projectile in terms of time?

Back

The height h(t) can be modeled by the equation h(t) = -16t² + vt + h₀, where v is the initial velocity and h₀ is the initial height.

Front

What does the coefficient of the x² term indicate in a quadratic function?

Back

The coefficient indicates the direction of the parabola: if positive, it opens upwards; if negative, it opens downwards.

Front

How can you find the time at which maximum height occurs in a projectile motion equation?

Back

Use the formula t = -b/(2a) from the standard form of the quadratic equation.

Front

What is the relationship between the vertex and the maximum or minimum value of a quadratic function?

Back

The vertex gives the maximum value if the parabola opens downwards and the minimum value if it opens upwards.

Front

How do you interpret the y-coordinate of the vertex in a real-world application?

Back

The y-coordinate of the vertex represents the maximum or minimum value of the quantity being modeled, such as height or profit.