Minimum And Maximum Point Of A Quadratic Equation

1. What is the minimum point and the corresponding value of x of the graph y=-(1-x)(x+2)?

Y=-1.5 and x=-2.85

Y= -2-25 and x=0.5

Y= 1.5 and x= 2.85

Y= -2.25 and x=-0.5

x-intercept, 1-x=0 and x+2=0

Therefore x₁=-2 and x₂₌₁. Take the Mid-Point of x₁and x₂to find the corresponding value of x.

Substitute into equation to find y. Answer (-0.5, -2.25)

Explanation

x-intercept, 1-x=0 and x+2=0

Therefore x₁=-2 and x₂₌₁. Take the Mid-Point of x₁and x₂to find the corresponding value of x.

Substitute into equation to find y. Answer (-0.5, -2.25)

2. What is the minimum point and the corresponding value of x of the graph y=1/2(x+3)(x-4)?

Y= 0.25 x=6.125

Y= -0.25 and x= -6.125

Y= -6.125 and x=0.5

Y=-12 and x=6.125

x-intercept, x+3=0 and x-4=0

Therefore x₁=-3 and x₂=4. Take the Mid-Point of x₁and x₂to find the corresponding value of x. Substitute into equation to find y. Answer (0.5, -6.125)

Explanation

x-intercept, x+3=0 and x-4=0

Therefore x₁=-3 and x₂=4. Take the Mid-Point of x₁and x₂to find the corresponding value of x. Substitute into equation to find y. Answer (0.5, -6.125)

3. What is the minimum point and the corresponding value of x of the graph y=1/4(x-2)(x-2)?

Y=0 and x=2

Y=0 and x=4

Y= -4 and x=2

Y=1/4 and x= 4

x-intercept, x-2=0. (A repeat root has only 1 value of x at the x-intercept.)

Therefore x=2. Substitute into equation to find y. Answer (3.25, -1.125)

Explanation

x-intercept, x-2=0. (A repeat root has only 1 value of x at the x-intercept.)

Therefore x=2. Substitute into equation to find y. Answer (3.25, -1.125)

4. What is the minimum point and the corresponding value of x of the graph y=2(x-3)²+6

Y=-6 and x=3

Y=6 and x=-3

Y=6 and x=3

Y=-6 and x=-3

At Minimum point, (x-3)²=0, Therefore y=6 when x=3

Explanation

At Minimum point, (x-3)²=0, Therefore y=6 when x=3

5. What is the maximum point and the corresponding value of x of the graph y=-3(x-1/2)²+3?

Y=3 and x= -1/2

Y= -3 and x=1/2

Y= -3 x= -1/2

Y=3 and x=1/2

At Maximum point, (x-1/2)²=0, Therefore y=3 when x=-1/2

Explanation

At Maximum point, (x-1/2)²=0, Therefore y=3 when x=-1/2

6. What is the maximum point and the corresponding value of x of the graph y=-4(x+2)²?

Y=0 and x=0

Y=0 and x=-2

Y=-4 and x=-2

At Maximum point, (x+2)²=0, Therefore y=0 when x=-2

Explanation

At Maximum point, (x+2)²=0, Therefore y=0 when x=-2

7. What is the minimum point and the corresponding value of x of the graph y=(x-4)(2x-5)?

Y=-1.125 and x= 3.25

Y=1.125 and x=-3.25

Y= 2.5 and x= 4

Y=-2.5 and x=-4

x-intercept, 2x-5=0 and x-4=0

Therefore x₁=5/2 and x₂=4. Take the Mid-Point of x₁and x₂to find the corresponding value of x. Substitute into equation to find y. Answer (3.25, -1.125)

Explanation

x-intercept, 2x-5=0 and x-4=0

Therefore x₁=5/2 and x₂=4. Take the Mid-Point of x₁and x₂to find the corresponding value of x. Substitute into equation to find y. Answer (3.25, -1.125)

8. What is the minimum point and the corresponding value of x of the graph y=4x²?

Y=0 and x=0

Y=0 and x=4

Y=4 and x=4

Y=4 and x=0

At Minimum point, 4x²=0, Therefore y=4 when x=0

Explanation

At Minimum point, 4x²=0, Therefore y=4 when x=0