6 (a) Complete the table of values for $y = x^2 - 3x + 1$ | $x$ | $-1$ | $0$ | $1$ | $2$ | $3$ | $4$ | |--------|-------|-------|-------|-------|-------|-------| | $y$ | $1$ | $1$ | $-1$ | $1$ | $5$ | $13$ | (b) On the grid, draw the graph of $y = x^2 - 3x + 1$ for values of $x$ from $-1$ to $4$. (c) Using your graph, find estimates for the solutions of the equation $x^2 - 3x + 1 = 0$.

GCSE Edexcel Maths Ratio Analysis and Problem Solving: 6 (a) Complete the table of valu

6 (a) Complete the table of values for $y = x^2 - 3x + 1$ | $x$ | $-1$ | $0$ | $1$ | $2$ | $3$ | $4$ | |--------|-------|-------|-------|-------|-------|-------| | $y$ | $1$ | $1$ | $-1$ | $1$ | $5$ | $13$ | (b) On the grid, draw the graph of $y = x^2 - 3x + 1$ for values of $x$ from $-1$ to $4$ - Edexcel - GCSE Maths - Question 7 - 2022 - Paper 1

Question 7

6-(a)-Complete-the-table-of-values-for-$y-=-x^2---3x-+-1$--|---$x$--|--$-1$--|--$0$--|--$1$--|--$2$--|--$3$--|--$4$--|-|--------|-------|-------|-------|-------|-------|-------|-|---$y$--|---$1$--|---$1$--|--$-1$--|---$1$--|---$5$--|--$13$--|--(b)-On-the-grid,-draw-the-graph-of-$y-=-x^2---3x-+-1$-for-values-of-$x$-from-$-1$-to-$4$-Edexcel-GCSE Maths-Question 7-2022-Paper 1.png

6 (a) Complete the table of values for $y = x^2 - 3x + 1$ | $x$ | $-1$ | $0$ | $1$ | $2$ | $3$ | $4$ | |--------|-------|-------|-------|-------|----... show full transcript

Worked Solution & Example Answer:6 (a) Complete the table of values for $y = x^2 - 3x + 1$ | $x$ | $-1$ | $0$ | $1$ | $2$ | $3$ | $4$ | |--------|-------|-------|-------|-------|-------|-------| | $y$ | $1$ | $1$ | $-1$ | $1$ | $5$ | $13$ | (b) On the grid, draw the graph of $y = x^2 - 3x + 1$ for values of $x$ from $-1$ to $4$ - Edexcel - GCSE Maths - Question 7 - 2022 - Paper 1

Step 1

Complete the table of values for $y = x^2 - 3x + 1$

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Answer

To complete the table, we will substitute each value of $x$ into the equation $y = x^2 - 3x + 1$ :

For $x = -1$ :
$y = (-1)^2 - 3(-1) + 1 = 1 + 3 + 1 = 5$
For $x = 0$ :
$y = (0)^2 - 3(0) + 1 = 0 - 0 + 1 = 1$
For $x = 1$ :
$y = (1)^2 - 3(1) + 1 = 1 - 3 + 1 = -1$
For $x = 2$ :
$y = (2)^2 - 3(2) + 1 = 4 - 6 + 1 = -1$
For $x = 3$ :
$y = (3)^2 - 3(3) + 1 = 9 - 9 + 1 = 1$
For $x = 4$ :
$y = (4)^2 - 3(4) + 1 = 16 - 12 + 1 = 5$

Thus, the completed table is:

$x$	$-1$	$0$	$1$	$2$	$3$	$4$
$y$	$5$	$1$	$-1$	$-1$	$1$	$5$

Step 2

On the grid, draw the graph of $y = x^2 - 3x + 1$

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Answer

To draw the graph, we will plot the points from the completed table:

Point at $(-1, 5)$
Point at $(0, 1)$
Point at $(1, -1)$
Point at $(2, -1)$
Point at $(3, 1)$
Point at $(4, 5)$

Next, we sketch a smooth curve through these points to represent the quadratic function.

Step 3

Using your graph, find estimates for the solutions of the equation $x^2 - 3x + 1 = 0$

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Answer

To find the solutions of $x^2 - 3x + 1 = 0$ , we look for the points where the graph intersects the x-axis (i.e., where $y = 0$ ):

From the graph, we can estimate the x-values at these points to be roughly:

$0.3$ (approximately)
$2.5$ (approximately)
These values represent the estimates for the solutions of the equation.

Complete the table of values for $y = x^2 - 3x + 1$

On the grid, draw the graph of $y = x^2 - 3x + 1$

Using your graph, find estimates for the solutions of the equation $x^2 - 3x + 1 = 0$

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