calculator, sketch the parabola $$ y=(x-1)(x+5) $$. Find the $$ y $$ value of the $$ y $$ - intercept. $$ y=-5 $$ Find the $$ x $$ values of the $$ x $$ - intercepts. Write all solutions on the same line separated by a comma. $$ \quad x=1,-5 $$ State the equation of the axis of symmetry. $$ \quad x=-2 $$ Find the coordinates of the turning point. Vertex $$ =(\square, ~ $$

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UpStudy AI · Accepted Answer

The coordinates of the turning point (vertex) are:

**Vertex = $$(-2, -9)$$**

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### Summary of the Parabola $$ y = (x - 1)(x + 5) $$:

1. **Y-intercept:** $$ y = -5 $$
2. **X-intercepts:** $$ x = 1, -5 $$
3. **Axis of Symmetry:** $$ x = -2 $$
4. **Vertex (Turning Point):** $$ (-2, -9) $$

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### Sketch of the Parabola:

To visualize the parabola, plot the intercepts and the vertex:

1. **Plot the Y-intercept** at $$ (0, -5) $$.
2. **Plot the X-intercepts** at $$ (1, 0) $$ and $$ (-5, 0) $$.
3. **Plot the Vertex** at $$ (-2, -9) $$.
4. **Draw the Axis of Symmetry** as a vertical line through $$ x = -2 $$.

The parabola opens upwards since the coefficient of $$ x^2 $$ is positive when you expand the equation:

$$ y = (x - 1)(x + 5) = x^2 + 4x - 5 $$

This confirms the shape and orientation of the parabola.
The turning point of the parabola $$ y = (x - 1)(x + 5) $$ is at $$ (-2, -9) $$.

calculator, sketch the
parabola
.
Find the value of the -
intercept.

Find the values of the -
intercepts.
Write all solutions on the same
line separated by a comma.

State the equation of the axis of
symmetry.

Find the coordinates of the
turning point.
Vertex

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calculator, sketch the parabola . Find the value of the - intercept. Find the values of the - intercepts. Write all solutions on the same line separated by a comma. State the equation of the axis of symmetry. Find the coordinates of the turning point. Vertex