Question

Help please I need 5 points total. i need 2 to left of vertex. i need vertex. i need 2 to right of vertex. Please, quickly, I am timed

graph only goes up to 14. thank you​

Answer 1

We are given with a quadratic equation which represents a Parabola , we need to find the vertex of the parabola , But let's recall that , For any quadratic equation of the form ax² + bx + c = 0 , the vertex of the parabola is given by ;

`{\quad \qquad \boxed{\bf{Vertex = \left((-b)/(2a),(-D)/(4a)\right)}}}`

Where , D = b² - 4ac (Discriminant)

Now , On comparing the given equation with ax² + bx + c , we have

⇢⇢⇢ a = 1 , b = - 10 , c = 27

Now , Calculating D ;

`{:\implies \quad \sf D=(-10)^(2)-4* 1* 27}`

`{:\implies \quad \sf D=100-108}`

`{:\implies \quad \bf \therefore \quad D=-8}`

Now , Calculating the vertex ;

`{:\implies \quad \sf Vertex =\bigg\{(-(-10))/(2* 1),(-(-8))/(4* 1)\bigg\}}`

`{:\implies \quad \sf Vertex = \left((10)/(2),(8)/(2)\right)}`

`{:\implies \quad \bf \therefore \quad Vertex = (5,2)}`

Hence , The vertex of the parabola is at (5,2)

Note :- As the Discriminant < 0 . So , the equation will have imaginary roots .

Refer to the attachment for the graph as well .