1 of 8 0-day streak

Connect factors with parabola features

Question 1 of 8

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The reference graph is \(y=x^2\)

The given quadratic is \(y = \frac{2}{3}(x+\frac{7}{2})(x+\frac{3}{2})\)

The output is denoted by g(x). Use exact values for every response

(a)1 mark

How is the given graph obtained from the basic quadratic graph y=x²?

Translate the graph \(\frac{5}{2}\) units to the left

Translate the graph \(\frac{2}{3}\) units down

Apply a vertical compression by factor \(\frac{2}{3}\)

Translate the graph \(\frac{5}{2}\) units to the left

Translate the graph \(\frac{2}{3}\) units down

Apply a vertical stretch by factor \(\frac{3}{2}\)

Translate the graph \(\frac{5}{2}\) units to the left

Translate the graph \(\frac{2}{3}\) units down

Apply a vertical compression by factor \(\frac{2}{3}\)

Translate the graph \(\frac{5}{2}\) units to the right

Translate the graph \(\frac{2}{3}\) units down

(b)3 marks

Give the turning-point coordinates and the x-value of the vertical symmetry line

\(x_V\) \(y_V\) Axis x-value

State the direction in which the parabola opens

The graph opens upward

The graph opens downward

(d)2 marks

Enter the exact x-coordinates of both x-intercepts in increasing order

\(x_1\) \(x_2\)