Express $4x^2 + 4x - 15$ in the form of $a(x + b)^2 + c$.[2] Hence, sketch the graph of \(y = 4x

Question

Express $4x^2 + 4x - 15$ in the form of $a(x + b)^2 + c$.[2] Hence, sketch the graph of $y = 4x^2 + 4x - 15$, indicating clearly the coordinates of the turning point and $y$-intercept.[3] Explain why another graph $y = -\left(x + \frac{1}{2}\right)^2 - 19$ will not intersect the graph of $y = 4x^2 + 4x - 15$.[2]

Accepted Answer

(a) $4\left(x+\frac12\right)^2-16$ (b) Turning point $\left(-\frac12,-16\right)$, $y$-intercept $(0,-15)$, $x$-intercepts $\left(-\frac52,0\right)$ and $\left(\frac32,0\right)$ (c) The graphs do not intersect

2023 CSS AM S3 EOY Q5

2023 CSS AM S3 EOY Q5

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