Question

h(x) = 2x² - 5x + 3

1. h(2) to h(4)

y = 2x² - 5x + 3

1. 3,1

f(x) = x² - 6x - 16

1. f(-2) to f(2)

f(x) = x² - 6x - 16

1. 5,4

Explanation:

Let's solve problem 5: \( h(2) \) to \( h(4) \) for \( h(x) = 2x^2 - 5x + 3 \)

Step 1: Calculate \( h(2) \)

Substitute \( x = 2 \) into \( h(x) \):
\( h(2) = 2(2)^2 - 5(2) + 3 \)
\( h(2) = 2(4) - 10 + 3 \)
\( h(2) = 8 - 10 + 3 \)
\( h(2) = 1 \)

Step 2: Calculate \( h(4) \)

Substitute \( x = 4 \) into \( h(x) \):
\( h(4) = 2(4)^2 - 5(4) + 3 \)
\( h(4) = 2(16) - 20 + 3 \)
\( h(4) = 32 - 20 + 3 \)
\( h(4) = 15 \)

Step 1: Calculate \( y \) at \( x = 3 \)

Substitute \( x = 3 \) into \( y = 2x^2 - 5x + 3 \):
\( y = 2(3)^2 - 5(3) + 3 \)
\( y = 2(9) - 15 + 3 \)
\( y = 18 - 15 + 3 \)
\( y = 6 \)

Step 2: Calculate \( y \) at \( x = 1 \)

Substitute \( x = 1 \) into \( y = 2x^2 - 5x + 3 \):
\( y = 2(1)^2 - 5(1) + 3 \)
\( y = 2(1) - 5 + 3 \)
\( y = 2 - 5 + 3 \)
\( y = 0 \)

Step 1: Calculate \( f(-2) \)

Substitute \( x = -2 \) into \( f(x) \):
\( f(-2) = (-2)^2 - 6(-2) - 16 \)
\( f(-2) = 4 + 12 - 16 \)
\( f(-2) = 0 \)

Step 2: Calculate \( f(2) \)

Substitute \( x = 2 \) into \( f(x) \):
\( f(2) = (2)^2 - 6(2) - 16 \)
\( f(2) = 4 - 12 - 16 \)
\( f(2) = -24 \)

Answer:

\( h(2) = 1 \), \( h(4) = 15 \)

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Let's solve problem 6: \( [3,1] \) for \( y = 2x^2 - 5x + 3 \) (assuming it's finding \( y \) at \( x = 3 \) and \( x = 1 \))