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)](https://tex.z-dn.net/?f=y%3D3%28x-1%29%28x%2B7%29)
<h3><u>Part (a)</u></h3>
<u>Intercept form of a quadratic equation</u>:
![y=a(x-p)(x-q)](https://tex.z-dn.net/?f=y%3Da%28x-p%29%28x-q%29)
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](https://tex.z-dn.net/?f=%5Cimplies%20%5Ctextsf%7BMidpoint%7D%3D%5Cdfrac%7Bx_2%2Bx_1%7D%7B2%7D%3D%5Cdfrac%7B1%2B%28-7%29%7D%7B2%7D%3D-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](https://tex.z-dn.net/?f=%5Cimplies%20y%3D3%28-3-1%29%28-3%2B7%29%3D-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