Question

Help is super appreciated this should probably be fast

2. Determine the y – intercept, zeros, the equation of the axis of symmetry and vertex of each quadratic
relation.
y = (x − 3)(x+3)

Answer 1

`\\ \rm\rightarrowtail y=(x-3)(x+3)=x^2-9`

Zeros are x intercepts

• (3,0) U(-3,0)

#2

• Y intercept=-9

#3

Axis of symmetry=x=0

#4

• Vertex=(0,-9)

Answer 2

Given quadratic equation: y = (x - 3)(x + 3)

Zeros (x-intercepts)

The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis. So the x-intercepts (zeros) are when y = 0

⇒ (x - 3)(x + 3) = 0

⇒ (x - 3) = 0 so x = 3

⇒ (x + 3) = 0 so x = -3

Therefore, the x-intercepts are at (3, 0) and (-3, 0).

y-intercept

The y-intercept is the point where the graph crosses the y-axis. So the y-intercept is when x = 0

⇒ (0 - 3)(0 + 3) = -9

Therefore, the y-intercept is at (0, -9)

Vertex

Expand the equation so that it is in standard form y = ax² + bx + c:

⇒ y = x² - 9

x-value of vertex is -b / 2a ⇒ -0 / 2 = 0

substitute the found value of x into the equation to find y:

⇒ y = (0)² - 9 = -9

Therefore, the vertex is (0, -9)

Axis of symmetry

Axis symmetry of a quadratic equation is x = a where a is the x-value of the vertex.

Therefore, the axis of symmetry is x = 0