Name: Range of Quadratic Expression
Uploaded: 2019-07-19
Duration: 26 min
Description: In this interesting video, we will understand how to find the range of quadratic expression using some interesting examples. Come, let's learn more!

Question

Find the equations of parabolas $A, B$ and $C$ .

Accepted Answer

Graph $A$ has its vertex at $(4, 2)$ . The point $(6, 6)$ lies on the curve.

There are no $x -$ intercepts.

Using $y = a (x - f)^{2} + g$ and substituting $f = 4, g = 2$

$\Rightarrow y = a (x - 4)^{2} + 2$

Now substituting $x = 6, y = 6$

$\Rightarrow 6 = a (6 - 4)^{2} + 2$

$\Rightarrow a = 1$

So, equation of parabola $A$ is $y = (x - 4)^{2} + 2$

Graph $B$ has its vertex at $(- 2, - 6)$

The $C$ -intercepts are not clear.

The point $(0, 10)$ lies on the curve.

Using $y = a (x - f)^{2} + g$ and substituting $f = - 2, g = - 6$

$\Rightarrow y = a (x - (- 2))^{2} - 6$

$\Rightarrow y = a (x + 2)^{2} - 6$

Now substituting $x = 0, y = 10$ gives

$10 = a (0 + 2)^{2} - 6$

$\Rightarrow a = 4$

So, equation of parabola $B$ is $y = 4 (x + 2)^{2} - 6$

Graph $C$ : There are more than three pieces of information which can be read off the graph e.g., the vertex is at $(2, 8)$

The $x$ -intercepts are $x = - 2, x = 6$

The point $(0, 6)$ lies on the curve etc.

Using $y = a (x - d) (x - e)$

Substituting $d = - 2, e = 6$ ,

$\Rightarrow y = a (x + 2) (x - 6)$

Now substituting $x = 2, y = 8$ gives

$8 = a (2 + 2) (2 - 6)$

$\Rightarrow a = - \frac{1}{2}$

So, equation of parabola $C$ is $y = - \frac{1}{2} (x + 2) (x - 6)$

Find the equations of parabolas $A, B$ and $C$ .

Important Questions on Quadratics

Learn and Prepare for any exam you want !

Find the equations of parabolas A, B and C.

Important Questions on Quadratics

Learn and Prepare for any exam you want !

Find the equations of parabolas $A, B$ and $C$ .