Question

Please help with this

Answer 1

Answer:

a) x = 1, x = -7

b) (-3, -48)

c) x = -3

d) upwards

Step-by-step explanation:

Given quadratic equation:

$y=3(x-1)(x+7)$

Part (a)

Intercept form of a quadratic equation:  

 $y=a(x-p)(x-q)$

where:

• p and q are the x-intercepts
• a is some constant

Comparing the formula with the given equation:

⇒ p = 1

⇒ q = -7

Therefore, the x-intercepts of the given equation are x = 1 and x = -7.

Part (b)

The midpoint between the two x-intercepts is the x-coordinate of the vertex.

$\implies \textsf{Midpoint}=\dfrac{x_2+x_1}{2}=\dfrac{1+(-7)}{2}=-3$

Therefore, the x coordinate of the vertex is -3.

To find the y-coordinate of the vertex, substitute this into the given equation:

$\implies y=3(-3-1)(-3+7)=-48$

Therefore, the coordinates of the vertex are (-3, -48).

Part (c)

The x-coordinate of the vertex is the axis of symmetry.

Therefore, the axis of symmetry is x = -3.

Part (d)

If the leading coefficient of a quadratic equation is positive, the parabola opens upwards.

If the leading coefficient of a quadratic equation is negative, the parabola opens downwards.

From inspection of the given equation, the leading coefficient is 3.

Therefore, the parabola opens upwards.

Learn more about quadratic equations here:

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