If f(x) = 2x² - 8x + 9, which statement regarding the vertex form of f(x) is true?

A.) In vertex form, f(x) = 2(x - 2)² + 1 and therefore has a minimum value of 1.

B.) In vertex form, f(x) = 2(x - 2)² + 1 and therefore has a minimum value of -2.

C.) In vertex form, f(x) = 2(x - 2)² + 4.5 and therefore has a minimum value of 4.5.

D.) In vertex form, f(x) = 2(x - 2)² + 4.5 and therefore has a minimum value of -2.

A.) In vertex form, f(x) = 2(x - 2)² + 1 and therefore has a minimum value of 1.

B.) In vertex form, f(x) = 2(x - 2)² + 1 and therefore has a minimum value of -2.

C.) In vertex form, f(x) = 2(x - 2)² + 4.5 and therefore has a minimum value of 4.5.

D.) In vertex form, f(x) = 2(x - 2)² + 4.5 and therefore has a minimum value of -2.

Standard form of a quadratic:f(x) = ax² + bx + cc is the y-intercept of the parabola |
Vertex form of a quadratic is:f(x) = a(x - h)² + k(h,k) are the coordinates of the vertex |

The equation f(x) = 2x² - 8x + 9 is in standard form and must be transformed into vertex form.

To begin, find the x and y coordinates of the vertex, then substitute them along with

*a*which is 2, into vertex form.

The x-coordinate of the vertex is

**x = -b / 2a**

In f(x) = 2x² - 8x + 9

a = 2, b = -8, and c = 9

x = -b/2a {the x-coordinate of the vertex}

x = -(-8) / 2(2) {substituted -8 for b and 2 for a into the x-coordinate of the vertex}

x = 8/4 {simplified and multiplied}

x = 2 {divided}

**The x-coordinate of the vertex is 2.**

To find the y-coordinate of the vertex, substitute 2 in for x into the equation f(x) = 2x² - 8x + 9.

f(x) = 2x² - 8x + 9 {original equation}

f(2) = 2(2)² - 8(2) + 9 {substituted 2 for x}

= 2(4) - 16 + 9 {evaluated exponent and multiplied}

= 8 - 16 + 9 {multiplied}

= 1 {subtracted and added}

**The y-coordinate of the vertex is 1.**

The vertex has coordinates of (2,1). In vertex form, these are the coordinates (h,k).

**Also the value of**

*a*is the same as in standard form, which is 2.f(x) = a(x - h)² + k {vertex form of a quadratic equation}

f(x) = 2(x - 2)² + 1 {substituted a,h, and k into vertex form}

In a parabola, which is the graph of a quadratic function, the y-coordinate of the vertex is either the minimum or maximum value. Since the leading coefficient, 2, is positive, this means the parabola opens upward, and thus has a minimum value.

**A.) In vertex form, f(x) = 2(x - 2)² + 1 and therefore has a minimum value of 1.**