Maths-

General

Easy

Question

# Find the axis of symmetry, vertex and y-intercept of the function

f(x) = -2x^{2} + 4x - 3

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 *y*-intercept is the point where a graph crosses the *y*-axis. In other words, it is the value of *y* when x=0.

## The correct answer is: -3

### This quadratic function is in standard form, f(x)=ax^{2}+bx+c.

For every quadratic function in standard form the axis of symmetry is given by the formula x=−b/2a.

In f(x)= -2x^{2} + 4x -3, a= -2, b= 4, and c= -3. So, the equation for the axis of symmetry is given by

x = −(4)/2(-2)

x = -4/-4

x = 1

The equation of the axis of symmetry for f(x)= 2x^{2} + 4x - 3 is x = 1.

The x coordinate of the vertex is the same:

h = 1

The y coordinate of the vertex is :

k = f(h)

k = -2(h)^{2} + 4(h) - 3

k = -2(1)^{2} + 4(1) - 3

k = -2 + 4 - 3

k = -1

Therefore, the vertex is (1 , -1)

For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

y = -2(0)^{2} + 4(0) - 3

y = 0 + 0 - 3

y = -3

Therefore, Axis of symmetry is x = 1

Vertex is ( 1 , -1)

Y- intercept is -3.

The equation of the axis of symmetry for f(x)= 2x

^{2}+ 4x - 3 is x = 1.

The x coordinate of the vertex is the same:

h = 1

The y coordinate of the vertex is :

^{2}+ 4(h) - 3

^{2}+ 4(1) - 3

Therefore, the vertex is (1 , -1)

For finding the y- intercept we firstly rewrite the equation by substituting 0 for x.

^{2}+ 4(0) - 3

Therefore, Axis of symmetry is x = 1

Vertex is ( 1 , -1)

Y- intercept is -3.

### Related Questions to study

Maths-

### Find the axis of symmetry, vertex and y-intercept of the function

f(x) = 2x^{2} + 8x + 2

### Find the axis of symmetry, vertex and y-intercept of the function

f(x) = 2x^{2} + 8x + 2

Maths-General

Maths-

### Find the y-intercept of the following function

f(x) = -0.5x^{2} + x + 2

### Find the y-intercept of the following function

f(x) = -0.5x^{2} + x + 2

Maths-General

Maths-

### Find the y-intercept of the following function

f(x) = - x^{2} – 2x + 3

### Find the y-intercept of the following function

f(x) = - x^{2} – 2x + 3

Maths-General

Maths-

### Find the y-intercept of the following function

f(x) = 3x^{2} + 6x + 5

### Find the y-intercept of the following function

f(x) = 3x^{2} + 6x + 5

Maths-General

Maths-

### Find the y-intercept of the following function

f(x) = -2x^{2} – 8x – 7

### Find the y-intercept of the following function

f(x) = -2x^{2} – 8x – 7

Maths-General

Maths-

### Find the y-intercept of the following function

f(x) = 0.3x^{2} + 0.6x – 0.7

### Find the y-intercept of the following function

f(x) = 0.3x^{2} + 0.6x – 0.7

Maths-General

Maths-

### Find the y-intercept of the following function

f(x) = 2x^{2} – 4x – 6

### Find the y-intercept of the following function

f(x) = 2x^{2} – 4x – 6

Maths-General

Maths-

### Points (2, -1), (-2, 7), (1, -2), (0, -1) and (4, 7) lie on graph of a quadratic function

1.Find axis of symmetry of graph

2.Find the vertex

3.Find the y-intercept

4.Over what interval does the function increase

### Points (2, -1), (-2, 7), (1, -2), (0, -1) and (4, 7) lie on graph of a quadratic function

1.Find axis of symmetry of graph

2.Find the vertex

3.Find the y-intercept

4.Over what interval does the function increase

Maths-General

Maths-

### Estimate the coordinates of the vertex of the graph of f(x) = 1.25x^{2} -2x -1 below. Then explain how to find the exact coordinates

### Estimate the coordinates of the vertex of the graph of f(x) = 1.25x^{2} -2x -1 below. Then explain how to find the exact coordinates

Maths-General

Maths-

### To identify the y-intercept of quadratic function, would you choose to use vertex form or standard form? Explain

### To identify the y-intercept of quadratic function, would you choose to use vertex form or standard form? Explain

Maths-General

Maths-

### A water balloon is tossed into the air. The function h(x) = -0.5(x-4)^{2} + 9 gives the height, in feet, of the balloon from the surface of a pool as a function of the balloon’s horizontal distance from where it was first tossed. Will the balloon hit the ceiling 12 ft above the pool? Explain

### A water balloon is tossed into the air. The function h(x) = -0.5(x-4)^{2} + 9 gives the height, in feet, of the balloon from the surface of a pool as a function of the balloon’s horizontal distance from where it was first tossed. Will the balloon hit the ceiling 12 ft above the pool? Explain

Maths-General

Maths-

### Sage began graphing f(x) = -2x^{2} + 4x + 9 by finding the axis of symmetry x = -1. Explain the error Sage made?

### Sage began graphing f(x) = -2x^{2} + 4x + 9 by finding the axis of symmetry x = -1. Explain the error Sage made?

Maths-General

Maths-

### How are the form and graph of f(x) = ax^{2} + bx + c similar to the form and graph of g(x) = ax^{2} + bx? How are they different?

### How are the form and graph of f(x) = ax^{2} + bx + c similar to the form and graph of g(x) = ax^{2} + bx? How are they different?

Maths-General

Maths-

### How is the standard form of a quadratic function different from vertex form?

### How is the standard form of a quadratic function different from vertex form?

Maths-General

Maths-

### Suppose the path of the ball in above figure is f(x) = -0.25(x-1)^{2} + 6.25. Find the ball’s initial and maximum heights.

### Suppose the path of the ball in above figure is f(x) = -0.25(x-1)^{2} + 6.25. Find the ball’s initial and maximum heights.

Maths-General