Question

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Answer 1

The shape of the graph of quadratic functions is the shape of a parabola.

The steps for drawing a graph of the function f(x) = 2·(x + 4)² - 3 arranged in the correct order are;

• (a) Plot the vertex (-4, -3)

• (b) Apply the 2·x² pattern, from the vertex go right 1 up 2 and plot (-3, -1)

• (c) Apply the 2·x² pattern again, from the vertex go right 2 up 8 and plot (-2, 5)

• (d) Apply the 2·x² pattern a 3rd time, from the vertex go right 3 up 18 and plot (-1, 15)

• (e) Draw the axis of symmetry x = -4

• (f) Reflect the points over the axis of symmetry and plot (-5, -1), (-6, 5), and (-7, 15)

• (g) Draw a U shaped parabola.

Reasons:

The given function is; f(x) = 2·(x + 4)² - 3

The function is given in the vertex form; f(x) = a·(x - h)² + k

Therefore, the vertex, (h, k) = (-4, -3)

Step (a);

The vertex can be plotted on the graph

• Plot the vertex (-4, -3)

Step (b);

Given that the quadratic term is 2·x², the pattern that can be used for the points from the vertex is therefore, 2·x²

From the vertex (-4, -3) apply the 2·x² pattern by going to the right 1 unit and  up 2 × 1² = 2 units to get the point (-4 + 1, -3 + 2) = (-3. -1)

• Apply the 2·x² pattern, from the vertex go right 1 up 2 and plot (-3, -1)

Step (c);

To get the next point, the 2·x² pattern is applied with x = 2, to the vertex to get; (-4 + 2, -3 + (2×2²)) = (-2, 5)

• Apply the 2·x² pattern again, from the vertex go right 2 up 8 and plot (-2, 5)

Step (d);

A third point on the graph relative to the vertex is obtained again by applying the 2·x² pattern again to the vertex with x = 3, to get;

(-4 + 3, -3 + (2 × 3²)) = (-1, 15)

• Apply the 2·x² pattern a 3rd time, from the vertex go right 3 up 18 and plot (-1, 15)

Step (e);

The axis of symmetry can be drawn with a vertical line passing through the vertex, which is the line, x = -4

The line x = -4 can be drawn on the graph next

• Draw the axis of symmetry x = -4

Step (f);

The points obtained relative to the vertex (-3, -1), (-2, 5), (-1, 15) can reflected about the axis of symmetry x = -4, to get;

(-3, -1) $\underrightarrow {R_{(x = -4)}}$ (-5, -1)

(-2, 5) $\underrightarrow {R_{(x = -4)}}$ (-7, 5)

(-1, 15) $\underrightarrow {R_{(x = -4)}}$ (-7, 15)

• Reflect the points over the axis of symmetry and plot (-5, -1), (-6, 5), and (-7, 15)

Step (g);

The parabola that is U shaped can be drawn from the points plotted in the steps above.

• Draw a U shaped parabola

Learn more about drawing the graph of a quadratic function here:

brainly.com/question/6353430