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x- and y-intercepts (2)

In this worksheet, students find the x- or y-intercepts of the given quadratic graph equations.

'x- and y-intercepts (2)' worksheet

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Identify and Interpret Roots, Intercepts and Turning Points of Quadratic Functions Graphically

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

The x-intercept is the point at which the given graph crosses:

the x-axis at (x, 0). 

This is where y = 0.

 

The y-intercept is the point at which the given graph crosses:

the y-axis at (0, y). 

This is where x = 0.

 

Example

Find the x- and y-intercepts of the graph with equation:

y = x2 + 4x + 3

 

Answer

We put y = 0 to get

x2 + 4x + 3 = 0

Factorise to get

(x + 3) (x + 1) = 0

x = -3 or -1

So the x-intercepts are at (-3, 0) and (-1, 0)

 

We put x = 0 to get

y = 0 + 0 + 3 = 3

So the y-intercept is (0, 3)

 

This can be checked on a graph as follows:

 

Find all the x-intercepts of the graph with equation

y = x2 - 1

(1, 0)

(-1, 0)

(0, 1)

(0, -1)

Find all the y-intercepts of the graph with equation

y = x2 - 1

(1, 0)

(-1, 0)

(0, 1)

(0, -1)

Find all the x-intercepts of the graph with equation

y = x2 + 3x

(3, 0)

(-3, 0)

(0, √3)

(0, 0)

Find all the y-intercepts of the graph with equation

y = x2 + 3x

(1, 0)

(-3, 0)

(0, -3)

(0, 0)

Find all the x-intercepts of the graph with equation

y = x2 - x - 6

(2, 0)

(-2, 0)

(3, 0)

(0, -3)

Find all the y-intercepts of the graph with equation

y = x2 - x - 6

(3, 0)

(-6, 0)

(0, -6)

(0, 6)

Find all the x-intercepts of the graph with equation

y = 4x2 + 3x - 1

(-1, 0)

(-1, ¼)

(0, ¼)

(¼, 0)

Find all the y-intercepts of the graph with equation

y = 4x2 + 3x - 1

(0, -1)

(-1, 0)

(0, 1)

(0, ¼)

Find all the x-intercepts of the graph with equation

y = 8x2 - 10x - 3

(1½, 0)

(-1½, 0)

(-4, 0)

(-¼, 0)

Find all the y-intercepts of the graph with equation

y = 8x2 - 10x - 3

(3, 0)

(-3, 0)

(0, -3)

(0, 3)

  • Question 1

Find all the x-intercepts of the graph with equation

y = x2 - 1

CORRECT ANSWER
(1, 0)
(-1, 0)
EDDIE SAYS
When y = 0,
x² - 1 = 0
(x - 1)(x + 1) = 0
x = ±1
  • Question 2

Find all the y-intercepts of the graph with equation

y = x2 - 1

CORRECT ANSWER
(0, -1)
EDDIE SAYS
When x = 0,
y = 0 - 1 = -1
  • Question 3

Find all the x-intercepts of the graph with equation

y = x2 + 3x

CORRECT ANSWER
(-3, 0)
(0, 0)
EDDIE SAYS
When y = 0,
x² + 3x = 0
x(x + 3) = 0
x = 0, -3
  • Question 4

Find all the y-intercepts of the graph with equation

y = x2 + 3x

CORRECT ANSWER
(0, 0)
EDDIE SAYS
When x = 0,
y = 0 + 0 = 0
  • Question 5

Find all the x-intercepts of the graph with equation

y = x2 - x - 6

CORRECT ANSWER
(-2, 0)
(3, 0)
EDDIE SAYS
When y = 0,
x² - x - 6 = 0
(x - 3)(x + 2) = 0
x = -2, 3
  • Question 6

Find all the y-intercepts of the graph with equation

y = x2 - x - 6

CORRECT ANSWER
(0, -6)
EDDIE SAYS
When x = 0,
y = 0 - 0 - 6 = -6
  • Question 7

Find all the x-intercepts of the graph with equation

y = 4x2 + 3x - 1

CORRECT ANSWER
(-1, 0)
(¼, 0)
EDDIE SAYS
When y = 0,
4x² + 3x - 1 = 0
(4x - 1)(x + 1) = 0
x = -1, ¼
  • Question 8

Find all the y-intercepts of the graph with equation

y = 4x2 + 3x - 1

CORRECT ANSWER
(0, -1)
EDDIE SAYS
When x = 0,
y = 0 + 0 - 1 = -1
  • Question 9

Find all the x-intercepts of the graph with equation

y = 8x2 - 10x - 3

CORRECT ANSWER
(1½, 0)
(-¼, 0)
EDDIE SAYS
When y = 0,
8x² - 10x - 3 = 0
(2x - 3)(4x + 1) = 0
x = -¼, 1½
  • Question 10

Find all the y-intercepts of the graph with equation

y = 8x2 - 10x - 3

CORRECT ANSWER
(0, -3)
EDDIE SAYS
When x = 0,
y = 0 - 0 - 3 = -3
---- OR ----

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