Question

The line of symmetry of the parabola whose equation is y = ax2 - 4x + 3 is x = -2. What is the value of "a"?

A.) -2
B.) -1 or
C.) -1/2

Answer 1

y=a(−2)^2−4(−2)+3

Squaring an expression is the same as multiplying the expression by itself 2 times.

y=(a⋅(−2)(−2))−4(−2)+3

Multiply to simplify the expression (−2)(−2).

y=(a⋅4)−4(−2)+3

Multiply a by 4 to get 4a.

y=(4a)−4(−2)+3

Multiply −4 by each term inside the parentheses.

y=(4a)+8+3

Remove the parentheses around the expression 4a.

y=4a+8+3

Add 3 to 8 to get 11.

y=4a+11

Since a is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.

4a+11=y

Since 11 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 11 from both sides.

4a=−11+y

Move all terms not containing a to the right-hand side of the equation.

4a=y−11

Divide each term in the equation by 4.

a=14y−114

Answer 2

Consider finding the roots of \[ax ^{2} - 4x +3 = 0\]
With a=-2 they are \[-1 +- \frac{ \sqrt{10} }{ 2 }\]
With a = -1 they are \[-2+- \sqrt{7}\]
With a = -1/2 they are \[-4 +- \sqrt{22}\]

In the second case, the roots are symmetric about x=-2; therefore, the parabola is too.

Answer 3

Thank You BillBell!

Answer 4

Welcome!

Answer 5

... and thank you for the medal.