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Ede4ka [16]
2 years ago
6

Please help with this

Mathematics
1 answer:
Nata [24]2 years ago
5 0

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)

<h3><u>Part (a)</u></h3>

<u>Intercept form of a quadratic equation</u>:  

 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.

<h3><u>Part (b)</u></h3>

The <u>midpoint</u> 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, <u>substitute</u> this into the given equation:

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

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

<h3><u>Part (c)</u></h3>

The <u>x-coordinate of the vertex</u> is the axis of symmetry.

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

<h3><u>Part (d)</u></h3>

If the <u>leading coefficient</u> of a quadratic equation is <u>positive</u>, the parabola opens upwards.

If the <u>leading coefficient</u> of a quadratic equation is <u>negative</u>, 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:

brainly.com/question/27997764

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