B.E.S.T. Algebra 1 — EOC Practice

Question 1 of 10

Florida standards 8A-8BMedium Calc Diagram

For a quadratic equation ax² + bx + c = 0, the discriminant is b² − 4ac. It tells us how many times the related parabola y = ax² + bx + c crosses the x-axis — and therefore how many real solutions the equation has.

The discriminant's sign matches the number of x-axis crossings.

Which statement about D = 0 is TRUE?

AThe number of solutions can't be determined from D alone

BExactly one real solution — the parabola is tangent to the x-axis

CNo real solutions — the parabola doesn't reach the x-axis

DTwo real solutions — the parabola crosses the x-axis twice

Explanation

The discriminant b² − 4ac counts how many real solutions a quadratic equation has by reflecting how many times the parabola y = ax² + bx + c crosses the x-axis.

The three cases:
• D > 0: parabola crosses the x-axis at TWO different points → 2 real solutions.
• D = 0: parabola is *tangent* to the x-axis — it touches at exactly ONE point (the vertex itself sits on the x-axis) → 1 real solution (often called a *double root*).
• D < 0: parabola sits entirely above or below the x-axis, never touching it → 0 real solutions (the roots are complex / imaginary).

Application: D = 0 is the borderline case useful for problems like "for what value of c does ax² + bx + c = 0 have exactly one solution?" — set b² − 4ac = 0 and solve.

Question 2 of 10

Florida standards 1A-1GEasy Calc

A square garden has an area of 64 square feet. If the side length is x feet, the relationship is x² = 64.

The algebra gives two mathematical solutions, but only one makes physical sense as a side length. Which choice gives BOTH algebraic solutions AND correctly identifies the physical side length?

Ax = ±8 algebraically; the garden's side length is +8 ft

BOnly x = 8 — that's the only solution to x² = 64

COnly x = −8, because squaring a negative gives a positive

Dx = 32, because half of 64 is the side length

Explanation

Taking the square root of both sides gives x = ±√64 = ±8, because both (+8)² = 64 AND (−8)² = 64. In pure algebra you must report both roots. For the physical garden, length can't be negative, so only +8 ft applies in context — but the algebraic answer set is {−8, +8}.

Common mistakes: (A) Dropping the negative root entirely. (D) Dividing 64 by 2 instead of taking a square root.

Tip: when you see x² = N, always write x = ±√N first, then decide which roots fit the real-world context.

Question 3 of 10

Florida standards 1A-1GMedium Calc Word

A car rental costs $25 per day plus $0.15 per mile. If the total cost is $70 for one day, how many miles were driven?

A300

B200

C250

D350

Explanation

📌 70 = 25 + 0.15m
45 = 0.15m
m = 300 miles

Question 4 of 10

Florida standards 2A-2HMedium Calc Word Diagram

Which line has a negative slope?

BNeither

DBoth

Explanation

📌 Negative slope = line goes DOWN from left to right (↘).
Positive slope = line goes UP from left to right (↗).
Graph B has negative slope.

Question 5 of 10

Florida standards 7A-7CEasy Calc Word Diagram

Which graph represents a quadratic function?

CBoth

DNeither

Explanation

📌 Quadratic = U-shaped parabola. Graph A shows a parabola.
Graph B is a straight line → linear, not quadratic.

Question 6 of 10

Florida standards 5A-5CHard Calc

Solve: 3x+4y=10, 2x−4y=−5

A(1, 1.75)

B(2, 1)

C(1, 2)

D(0, 2.5)

Explanation

📌 Add: 5x=5 → x=1. 3(1)+4y=10 → 4y=7 → y=7/4=1.75

Question 7 of 10

Florida standards 5A-5CMedium Calc Word Diagram

The graph shows two lines. What is the solution to the system?

A(2, 3)

B(0, 1)

C(1, 2)

D(3, 0)

Explanation

📌 The solution is where the lines intersect = (1, 2).
Verify: y = x + 1 → 2 = 1 + 1 ✓
y = −x + 3 → 2 = −1 + 3 ✓

Question 8 of 10

Florida standards 6A-6CMedium Calc

Factor: x² + 5x + 6

A(x+3)(x+3)

B(x+2)(x+3)

C(x−2)(x−3)

D(x+1)(x+6)

Explanation

📌 Find two numbers that multiply to 6 and add to 5: 2 and 3.
(x + 2)(x + 3)

Question 9 of 10

Florida standards 6A-6CMedium Calc Word Diagram

The parabola in the graph below has a vertex at which point?

A(2, 1)

B(0, 0)

C(1, -2)

D(-1, 2)

Explanation

The vertex is the lowest point of an upward-opening parabola, marked at approximately (1, -2).

Question 10 of 10

Florida standards 3A-3GEasy Calc Word Diagram

Which graph represents y = 2x + 1?

ANeither

CBoth

Explanation

📌 y = 2x + 1:
• Slope = 2 (positive → goes UP)
• y-intercept = 1 (crosses y-axis above origin)
Graph A shows positive slope with y-intercept above origin.

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