Quadratic Functions

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Math › Quadratic Functions

Questions 1 - 10

Find the center and radius of the circle defined by the equation:

$\left ( 3,-5 \right )\ and\ r=6$

$\left ( 3,5 \right )\ and\ r=6$

$\left ( -3,-5 \right )\ and\ r=18$

$\left ( -3,5 \right )\ and\ r=18$

$\left ( -3,5 \right )\ and\ r=6$

Explanation

The equation of a circle is: $(x-x_{1})^2+(y-y_{1})^2=r^2$ where is the radius and $(x_{1},y_{1})$ is the center.

In this problem, the equation is already in the format required to determine center and radius. To find the -coordinate of the center, we must find the value of that makes equal to 0, which is 3. We do the same to find the y-coordinate of the center and find that . To find the radius we take the square root of the constant on the right side of the equation which is 6.

Based on the figure below, which line depicts a quadratic function?

Red line

Blue line

Green line

Purple line

None of them

Explanation

A parabola is one example of a quadratic function, regardless of whether it points upwards or downwards.

The red line represents a quadratic function and will have a formula similar to $\small {f(x)=ax^2+bx+c}$ .

The blue line represents a linear function and will have a formula similar to $\small {f(x)=ax+b$ .

The green line represents an exponential function and will have a formula similar to $\small {f(x)=ax^b}$ .

The purple line represents an absolute value function and will have a formula similar to $\small {f(x)=\left |ax+b \right |}.$ .

Find the center and radius of the circle defined by the equation:

$\left ( 3,-5 \right )\ and\ r=6$

$\left ( 3,5 \right )\ and\ r=6$

$\left ( -3,-5 \right )\ and\ r=18$

$\left ( -3,5 \right )\ and\ r=18$

$\left ( -3,5 \right )\ and\ r=6$

Explanation

The equation of a circle is: $(x-x_{1})^2+(y-y_{1})^2=r^2$ where is the radius and $(x_{1},y_{1})$ is the center.

Find the center and radius of the circle defined by the equation:

$\left ( 3,-5 \right )\ and\ r=6$

$\left ( 3,5 \right )\ and\ r=6$

$\left ( -3,-5 \right )\ and\ r=18$

$\left ( -3,5 \right )\ and\ r=18$

$\left ( -3,5 \right )\ and\ r=6$

Explanation

The equation of a circle is: $(x-x_{1})^2+(y-y_{1})^2=r^2$ where is the radius and $(x_{1},y_{1})$ is the center.

Based on the figure below, which line depicts a quadratic function?

Red line

Blue line

Green line

Purple line

None of them

Explanation

A parabola is one example of a quadratic function, regardless of whether it points upwards or downwards.

The red line represents a quadratic function and will have a formula similar to $\small {f(x)=ax^2+bx+c}$ .

The blue line represents a linear function and will have a formula similar to $\small {f(x)=ax+b$ .

The green line represents an exponential function and will have a formula similar to $\small {f(x)=ax^b}$ .

The purple line represents an absolute value function and will have a formula similar to $\small {f(x)=\left |ax+b \right |}.$ .

Based on the figure below, which line depicts a quadratic function?

Red line

Blue line

Green line

Purple line

None of them

Explanation

A parabola is one example of a quadratic function, regardless of whether it points upwards or downwards.

The red line represents a quadratic function and will have a formula similar to $\small {f(x)=ax^2+bx+c}$ .

The blue line represents a linear function and will have a formula similar to $\small {f(x)=ax+b$ .

The green line represents an exponential function and will have a formula similar to $\small {f(x)=ax^b}$ .

The purple line represents an absolute value function and will have a formula similar to $\small {f(x)=\left |ax+b \right |}.$ .

Which of the following functions represents a parabola?

$f(x) = x^{2} - 9$

$f(x) = \frac{4x^{2}}{x^{3}}$

$f(x) = x^{2} - y^{2}$

Explanation

A parabola is a curve that can be represented by a quadratic equation. The only quadratic here is represented by the function $f(x) = x^{2} - 9$ , while the others represent straight lines, circles, and other curves.

Find the center and radius of the circle defined by the equation:

$(x+12)^{2}+(y+10)^2=100$

$\left ( -12,-10 \right )\ and\ r=10$

$\left ( 10,-12 \right )\ and\ r=100$

$\left ( 12,-10 \right )\ and\ r=10$

$\left ( -12,10 \right )\ and\ r=25$

$\left ( 12,-10 \right )\ and\ r=100$

Explanation

The equation of a circle is: $(x-x_{1})^2+(y-y_{1})^2=r^2$ where is the radius and $(x_{1},y_{1})$ is the center.

In this problem, the equation is already in the format required to determine center and radius. To find the -coordinate of the center, we must find the value of that makes equal to , which is . We do the same to find the y-coordinate of the center and find that . To find the radius we take the square root of the constant on the right side of the equation which is 10.