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Here is the graph of $y = -x^2 + 6x - 4$ - Edexcel - GCSE Maths - Question 7 - 2022 - Paper 2

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Question 7

Here-is-the-graph-of-$y-=--x^2-+-6x---4$-Edexcel-GCSE Maths-Question 7-2022-Paper 2.png

Here is the graph of $y = -x^2 + 6x - 4$. (a) Write down the $y$ intercept of the graph of $y = -x^2 + 6x - 4$. (b) Write down the coordinates of the turning poin... show full transcript

Worked Solution & Example Answer:Here is the graph of $y = -x^2 + 6x - 4$ - Edexcel - GCSE Maths - Question 7 - 2022 - Paper 2

Step 1

Write down the $y$ intercept of the graph of $y = -x^2 + 6x - 4$

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Answer

To find the yy-intercept, set x=0x = 0 in the equation:

y=−02+6(0)−4=−4y = -0^2 + 6(0) - 4 = -4

Thus, the yy-intercept is −4-4.

Step 2

Write down the coordinates of the turning point of the graph of $y = -x^2 + 6x - 4$

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Answer

The turning point can be found using the vertex formula x=−b2ax = -\frac{b}{2a} for a quadratic equation in the form ax2+bx+cax^2 + bx + c. Here, a=−1a = -1 and b=6b = 6:

x=−62(−1)=3x = -\frac{6}{2(-1)} = 3

Substituting x=3x = 3 back into the equation to find yy:

y=−(3)2+6(3)−4=−9+18−4=5y = -(3)^2 + 6(3) - 4 = -9 + 18 - 4 = 5

Thus, the coordinates of the turning point are (3,5)(3, 5).

Step 3

Use the graph to find estimates for the roots of $-x^2 + 6x - 4 = 0$

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Answer

From the graph, the roots can be estimated by observing where the curve intersects the xx-axis. These intersections appear to occur around x≈1x ≈ 1 and x≈5x ≈ 5. Hence, the estimated roots are approximately 11 and 55.

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