Maths-

General

Easy

Question

# Graph the function f(x)= -3x^{2} +12x+5

Hint:

### For a quadratic function is in standard form, f(x)=ax2+bx+c.

A vertical line passing through the vertex is called the axis of symmetry for the parabola.

Axis of symmetry x=−b/2a

Vertex The vertex of the parabola is located at a pair of coordinates which we will call (*h, k*). where h is value of x in axis of symmetry formula and k is f(h).

## The correct answer is: (2 , 17)

### We have given a function

f(x)= -3x^{2}+12x+5

We have to draw graph of given function,

For drawing graph we will need to find some points on curves

Firstly we will find vertex of the function,

x = -b/2a

= -(12)/2(-3)

= -12 / -6

= 2

The x coordinate of the vertex is the same:

h = 2

The y coordinate of the vertex is :

k = f(h)

k = -3h^{2} + 12h + 5

k = -3(2)^{2} + 12(2) + 5

k = -12 + 24 + 5

k = 17

Therefore, the vertex is (2 , 17)

Select a few x values, and plug them into the equation to find the corresponding y values. The x values should be selected around the vertex.

x

y

0

5

1

14

2

17

3

14

4

5

Plot the obtained points and draw the graph

x

y

0

5

1

14

2

17

3

14

4

5

### Related Questions to study

Maths-

### Identify the y – intercept , axis of symmetry , and vertex of the graph of each function . H(x)= -3x^{2}+7x+1

### Identify the y – intercept , axis of symmetry , and vertex of the graph of each function . H(x)= -3x^{2}+7x+1

Maths-General

Maths-

### Identify the y – intercept , axis of symmetry , and vertex of the graph of each function . G(x)= -x^{2}+4x+5

### Identify the y – intercept , axis of symmetry , and vertex of the graph of each function . G(x)= -x^{2}+4x+5

Maths-General

Maths-

### Graph the function f(x)= 3x^{2}-6x+2

### Graph the function f(x)= 3x^{2}-6x+2

Maths-General

Maths-

### Two models are used to predict monthly revenue for a new sports drink. In each model, x is the number of $1 – price increases from the original $2 per bottle price.

Model A : f(x)= -12.5 x^{2}+75x+200

Model B:

### Two models are used to predict monthly revenue for a new sports drink. In each model, x is the number of $1 – price increases from the original $2 per bottle price.

Model A : f(x)= -12.5 x^{2}+75x+200

Model B:

Maths-General

Maths-

### What is the maximum value of f(x)= -4x^{2} +16x+12

### What is the maximum value of f(x)= -4x^{2} +16x+12

Maths-General

Maths-

### An object is launched at 64 ft per second from an elevated platform , The Quadratic function shown in the table model its trajectory f(x) over time, x, select all the true statements .

X |
0 |
1 |
2 |
4 |

F(x) |
6 |
54 |
70 |
6 |

### An object is launched at 64 ft per second from an elevated platform , The Quadratic function shown in the table model its trajectory f(x) over time, x, select all the true statements .

X |
0 |
1 |
2 |
4 |

F(x) |
6 |
54 |
70 |
6 |

Maths-General

Maths-

### A banner is hung for a party . The distance from a point on the bottom edge of the banner to the floor can be determined by using the function f(x)= 0.25x^{2} -x+9.5, where x is the distance , in feet , of the point from the left end of the banner . How high above the floor is the lowest point on the bottom edge of the banner , Explain.

### A banner is hung for a party . The distance from a point on the bottom edge of the banner to the floor can be determined by using the function f(x)= 0.25x^{2} -x+9.5, where x is the distance , in feet , of the point from the left end of the banner . How high above the floor is the lowest point on the bottom edge of the banner , Explain.

Maths-General

Maths-

### The position of a ball after it is kicked can be determined by using the function f(x)= -0.11 x^{2}+2.2x+1, where y is the height , in feet , above the ground and x is the horizontal distance , in feet above the ground and x is the horizontal distance, in feet, of the ball from the point at which it was kicked . What is the height of the ball when it is kicked ? What is the highest point of the ball in the air ?

### The position of a ball after it is kicked can be determined by using the function f(x)= -0.11 x^{2}+2.2x+1, where y is the height , in feet , above the ground and x is the horizontal distance , in feet above the ground and x is the horizontal distance, in feet, of the ball from the point at which it was kicked . What is the height of the ball when it is kicked ? What is the highest point of the ball in the air ?

Maths-General

Maths-